Tootfinder

Sampling Problems on a Quantum Computer
Maximilian Balthasar Mansky, Jonas N\"u{\ss}lein, David Bucher, Dani\"elle Schuman, Sebastian Zielinski, Claudia Linnhoff-Popien
https://arxiv.org/abs/2402.16341

Sampling Problems on a Quantum Computer
Due to the advances in the manufacturing of quantum hardware in the recent years, significant research efforts have been directed towards employing quantum methods to solving problems in various areas of interest. Thus a plethora of novel quantum methods have been developed in recent years. In this paper, we provide a survey of quantum sampling methods alongside needed theory and applications of those sampling methods as a starting point for research in this area. This work focuses in particula…

Moving higher-order Taylor approximations method for smooth constrained minimization problems
Yassine Nabou, Ion Necoara
https://arxiv.org/abs/2402.15022 h…

Moving higher-order Taylor approximations method for smooth constrained minimization problems
In this paper we develop a higher-order method for solving composite (non)convex minimization problems with smooth (non)convex functional constraints. At each iteration our method approximates the smooth part of the objective function and of the constraints by higher-order Taylor approximations, leading to a moving Taylor approximation method (MTA). We present convergence guarantees for MTA algorithm for both, nonconvex and convex problems. In particular, when the objective and the constraints …

An Efficient Reconstructed Differential Evolution Variant by Some of the Current State-of-the-art Strategies for Solving Single Objective Bound Constrained Problems
Sichen Tao, Ruihan Zhao, Kaiyu Wang, Shangce Gao
https://arxiv.org/abs/2404.16280

An Efficient Reconstructed Differential Evolution Variant by Some of the Current State-of-the-art Strategies for Solving Single Objective Bound Constrained Problems
Complex single-objective bounded problems are often difficult to solve. In evolutionary computation methods, since the proposal of differential evolution algorithm in 1997, it has been widely studied and developed due to its simplicity and efficiency. These developments include various adaptive strategies, operator improvements, and the introduction of other search methods. After 2014, research based on LSHADE has also been widely studied by researchers. However, although recently proposed impr…

Graph-accelerated non-intrusive polynomial chaos expansion using partially tensor-structured quadrature rules
Bingran Wang, Nicholas C. Orndorff, John T. Hwang
https://arxiv.org/abs/2403.15614

Graph-accelerated non-intrusive polynomial chaos expansion using partially tensor-structured quadrature rules
Recently, the graph-accelerated non-intrusive polynomial chaos (NIPC) method has been proposed for solving uncertainty quantification (UQ) problems. This method leverages the full-grid integration-based NIPC method to address UQ problems while employing the computational graph transformation approach, AMTC, to accelerate the tensor-grid evaluations. This method exhibits remarkable efficacy on a broad range of low-dimensional (three dimensions or less) UQ problems featuring multidisciplinary mod…

Navigating Complexity: Orchestrated Problem Solving with Multi-Agent LLMs
Sumedh Rasal, E. J. Hauer
https://arxiv.org/abs/2402.16713 https://

Navigating Complexity: Orchestrated Problem Solving with Multi-Agent LLMs
Large Language Models (LLMs) have demonstrated remarkable capabilities in solving various tasks, yet they often struggle with comprehensively addressing complex and vague problems. Existing approaches, including multi-agent LLM systems, offer solutions to certain challenges but still require manual setup and lack scalability. To address this gap, we propose a novel approach leveraging decomposition to enable LLMs to tackle vague problems effectively. Our approach involves an orchestrating LLM…

Sampling Problems on a Quantum Computer
Maximilian Balthasar Mansky, Jonas N\"u{\ss}lein, David Bucher, Dani\"elle Schuman, Sebastian Zielinski, Claudia Linnhoff-Popien
https://arxiv.org/abs/2402.16341

Sampling Problems on a Quantum Computer
Due to the advances in the manufacturing of quantum hardware in the recent years, significant research efforts have been directed towards employing quantum methods to solving problems in various areas of interest. Thus a plethora of novel quantum methods have been developed in recent years. In this paper, we provide a survey of quantum sampling methods alongside needed theory and applications of those sampling methods as a starting point for research in this area. This work focuses in particula…

This https://arxiv.org/abs/2309.17027 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Unfitted Spectral Element Method for interfacial models
In this paper, we propose the unfitted spectral element method for solving elliptic interface and corresponding eigenvalue problems. The novelty of the proposed method lies in its combination of the spectral accuracy of the spectral element method and the flexibility of the unfitted Nitsche's method. We also use tailored ghost penalty terms to enhance its robustness. We establish optimal $hp$ convergence rates for both elliptic interface problems and interface eigenvalue problems. Additionally,…

Distributed MPC for PWA Systems Based on Switching ADMM
Samuel Mallick, Azita Dabiri, Bart De Schutter
https://arxiv.org/abs/2404.16712 https://

Distributed MPC for PWA Systems Based on Switching ADMM
This paper presents a novel approach for distributed model predictive control (MPC) for piecewise affine (PWA) systems. Existing approaches rely on solving mixed-integer optimization problems, requiring significant computation power or time. We propose a distributed MPC scheme that requires solving only convex optimization problems. The key contribution is a novel method, based on the alternating direction method of multipliers, for solving the non-convex optimal control problem that arises due…

Large language models can help boost food production, but be mindful of their risks
Djavan De Clercq, Elias Nehring, Harry Mayne, Adam Mahdi
https://arxiv.org/abs/2403.15475

Large language models can help boost food production, but be mindful of their risks
Coverage of ChatGPT-style large language models (LLMs) in the media has focused on their eye-catching achievements, including solving advanced mathematical problems and reaching expert proficiency in medical examinations. But the gradual adoption of LLMs in agriculture, an industry which touches every human life, has received much less public scrutiny. In this short perspective, we examine risks and opportunities related to more widespread adoption of language models in food production systems.…

This https://arxiv.org/abs/2207.05072 has been replaced.
link: https://scholar.google.com/scholar?q=a

An On-demand Photonic Ising Machine with Simplified Hamiltonian Calculation by Phase encoding and Intensity Detection
The photonic Ising machine is a new paradigm of optical computing that takes advantage of the unique properties of light wave propagation, parallel processing, and low-loss transmission. Thus, the process of solving combinatorial optimization problems can be accelerated through photonic/optoelectronic devices. In this work, we have proposed and demonstrated the Phase Encoding and Intensity Detection Ising Annealer (PEIDIA) capable of solving arbitrary Ising problems on demand. The PEIDIA employ…

Graph-accelerated non-intrusive polynomial chaos expansion using partially tensor-structured quadrature rules
Bingran Wang, Nicholas C. Orndorff, John T. Hwang
https://arxiv.org/abs/2403.15614

Graph-accelerated non-intrusive polynomial chaos expansion using partially tensor-structured quadrature rules
Recently, the graph-accelerated non-intrusive polynomial chaos (NIPC) method has been proposed for solving uncertainty quantification (UQ) problems. This method leverages the full-grid integration-based NIPC method to address UQ problems while employing the computational graph transformation approach, AMTC, to accelerate the tensor-grid evaluations. This method exhibits remarkable efficacy on a broad range of low-dimensional (three dimensions or less) UQ problems featuring multidisciplinary mod…

An Encoding for CLP Problems in SMT-LIB
Daneshvar Amrollahi, Hossein Hojjat, Philipp R\"ummer
https://arxiv.org/abs/2404.14924 https://

An Encoding for CLP Problems in SMT-LIB
The input language for today's CHC solvers are commonly the standard SMT-LIB format, borrowed from SMT solvers, and the Prolog format that stems from Constraint-Logic Programming (CLP). This paper presents a new front-end of the Eldarica CHC solver that allows inputs in the Prolog language. We give a formal translation of a subset of Prolog into the SMT-LIB commands. Our initial experiments show the effectiveness of the approach and the potential benefits to both the CHC solving and CLP communi…

This https://arxiv.org/abs/2404.05410 has been replaced.
initial toot: https://mastoxiv.page/@arX…

Solving quantum impurity problems on the L-shaped Kadanoff-Baym contour
The path integral formalism is the building block of many powerful numerical methods for quantum impurity problems. However, existing fermionic path integral based numerical calculations have only been performed in either the imaginary-time or the real-time axis, while the most generic scenario formulated on the L-shaped Kadanoff-Baym contour is left unexplored. In this work, we extended the recently developed Grassmann time-evolving matrix product operator (GTEMPO) method to solve quantum impu…

This https://arxiv.org/abs/2311.00259 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csLG_…

Solutions to Elliptic and Parabolic Problems via Finite Difference Based Unsupervised Small Linear Convolutional Neural Networks
In recent years, there has been a growing interest in leveraging deep learning and neural networks to address scientific problems, particularly in solving partial differential equations (PDEs). However, many neural network-based methods like PINNs rely on auto differentiation and sampling collocation points, leading to a lack of interpretability and lower accuracy than traditional numerical methods. As a result, we propose a fully unsupervised approach, requiring no training data, to estimate f…

The Sample Average Approximation Method for Solving Two-Stage Stochastic Programs with Endogenous Uncertainty
Maria Bazotte, Margarida Carvalho, Thibaut Vidal
https://arxiv.org/abs/2402.15486

The Sample Average Approximation Method for Solving Two-Stage Stochastic Programs with Endogenous Uncertainty
Real-world decision-making problems involve Type 1 decision-dependent uncertainty, where the probability distribution of the stochastic process depends on the model decisions. However, few studies focus on two-stage stochastic programs with this type of endogenous uncertainty, and those that do lack general methodologies. We thus propose herein a general method for solving a class of these programs based on the transformation of random variables, a technique widely employed in probability and s…

This https://arxiv.org/abs/2309.15271 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csRO_…

Kinematic Modularity of Elementary Dynamic Actions
In this paper, a kinematically modular approach to robot control is presented. The method involves structures called Elementary Dynamic Actions and a network model combining these elements. With this control framework, a rich repertoire of movements can be generated by combination of basic modules. The problems of solving inverse kinematics, managing kinematic singularity and kinematic redundancy are avoided. The modular approach is robust against contact and physical interaction, which makes i…

PI-CoF: A Bilevel Optimization Framework for Solving Active Learning Problems using Physics-Information
Liqiu Dong, Marta Zagorowska, Tong Liu, Alex Durkin, Mehmet Mercang\"oz
https://arxiv.org/abs/2402.13588

PI-CoF: A Bilevel Optimization Framework for Solving Active Learning Problems using Physics-Information
Physics informed neural networks (PINNs) have recently been proposed as surrogate models for solving process optimization problems. However, in an active learning setting collecting enough data for reliably training PINNs poses a challenge. This study proposes a broadly applicable method for incorporating physics information into existing machine learning (ML) models of any type. The proposed method - referred to as PI-CoF for Physics-Informed Correction Factors - introduces additive or multipl…

From Large to Tiny: Distilling and Refining Mathematical Expertise for Math Word Problems with Weakly Supervision
Qingwen Lin, Boyan Xu, Zhengting Huang, Ruichu Cai
https://arxiv.org/abs/2403.14390

From Large to Tiny: Distilling and Refining Mathematical Expertise for Math Word Problems with Weakly Supervision
Addressing the challenge of high annotation costs in solving Math Word Problems (MWPs) through full supervision with intermediate equations, recent works have proposed weakly supervised task settings that rely solely on the final answer as a supervised signal. Existing leading approaches typically employ various search techniques to infer intermediate equations, but cannot ensure their semantic consistency with natural language descriptions. The rise of Large Language Models (LLMs) like ChatGPT…

Incorporating Graph Attention Mechanism into Geometric Problem Solving Based on Deep Reinforcement Learning
Xiuqin Zhong, Shengyuan Yan, Gongqi Lin, Hongguang Fu, Liang Xu, Siwen Jiang, Lei Huang, Wei Fang
https://arxiv.org/abs/2403.14690

Incorporating Graph Attention Mechanism into Geometric Problem Solving Based on Deep Reinforcement Learning
In the context of online education, designing an automatic solver for geometric problems has been considered a crucial step towards general math Artificial Intelligence (AI), empowered by natural language understanding and traditional logical inference. In most instances, problems are addressed by adding auxiliary components such as lines or points. However, adding auxiliary components automatically is challenging due to the complexity in selecting suitable auxiliary components especially when …

Today has been a very busy day of problem solving. I just realized that with reading logs, diagnosing errors, contacting folks to report data problems, waiting for the data fixes, re-running, repeat... while I was very busy and productive, I didn't read or write a single line of program code today.
I don't think I've been consciously aware of it before today, but I think this happens a lot in the predictive-model implementation role.

Grasper: A Generalist Pursuer for Pursuit-Evasion Problems
Pengdeng Li, Shuxin Li, Xinrun Wang, Jakub Cerny, Youzhi Zhang, Stephen McAleer, Hau Chan, Bo An
https://arxiv.org/abs/2404.12626

Grasper: A Generalist Pursuer for Pursuit-Evasion Problems
Pursuit-evasion games (PEGs) model interactions between a team of pursuers and an evader in graph-based environments such as urban street networks. Recent advancements have demonstrated the effectiveness of the pre-training and fine-tuning paradigm in PSRO to improve scalability in solving large-scale PEGs. However, these methods primarily focus on specific PEGs with fixed initial conditions that may vary substantially in real-world scenarios, which significantly hinders the applicability of th…

This https://arxiv.org/abs/2310.12541 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csNE_…

Large Language Model for Multi-objective Evolutionary Optimization
Multiobjective evolutionary algorithms (MOEAs) are major methods for solving multiobjective optimization problems (MOPs). Many MOEAs have been proposed in the past decades, of which the search operators need a carefully handcrafted design with domain knowledge. Recently, some attempts have been made to replace the manually designed operators in MOEAs with learning-based operators (e.g., neural network models). However, much effort is still required for designing and training such models, and th…

This https://arxiv.org/abs/2402.07064 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Exact Semi-Definite Programs for Piecewise SOS-Convex Moment Optimization and Applications
In this paper, we present exact Semi-Definite Program (SDP) reformulations for a broad class of infinite-dimensional moment optimization problems involving piecewise Sums-of-Squares (SOS) convex polynomials and projected spectrahedral support sets. These reformulations show that the optimal value of the original moment problem can be found by solving a single SDP. In particular, we show how an optimal probability measure is recovered for these problems by solving a single SDP. This is done by f…

Integer Programming Using A Single Atom
Kapil Goswami, Peter Schmelcher, Rick Mukherjee
https://arxiv.org/abs/2402.16541 https://arxi…

Integer Programming Using A Single Atom
Integer programming (IP), as the name suggests is an integer-variable-based approach commonly used to formulate real-world optimization problems with constraints. Currently, quantum algorithms reformulate the IP into an unconstrained form through the use of binary variables, which is an indirect and resource-consuming way of solving it. We develop an algorithm that maps and solves an IP problem in its original form to any quantum system that possesses a large number of accessible internal degre…

Solving a Real-World Package Delivery Routing Problem Using Quantum Annealers
Eneko Osaba, Esther Villar-Rodriguez, Ant\'on Asla
https://arxiv.org/abs/2403.15114

Solving a Real-World Package Delivery Routing Problem Using Quantum Annealers
Research focused on the conjunction between quantum computing and routing problems has been very prolific in recent years. Most of the works revolve around classical problems such as the Traveling Salesman Problem or the Vehicle Routing Problem. Even though working on these problems is valuable, it is also undeniable that their academic-oriented nature falls short of real-world requirements. The main objective of this research is to present a solving method for realistic instances, avoiding pro…

This https://arxiv.org/abs/2403.13123 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

On incomplete Cholesky factorizations in half precision arithmetic
Incomplete factorizations have long been popular general-purpose algebraic preconditioners for solving large sparse linear systems of equations. Guaranteeing the factorization is breakdown free while computing a high quality preconditioner is challenging. A resurgence of interest in using low precision arithmetic makes the search for robustness more urgent and tougher. In this paper, we focus on symmetric positive definite problems and explore a number of approaches: a look-ahead strategy to an…

Hybrid deep learning and physics-based neural network for programmable illumination computational microscopy
Ruiqing Sun, Delong Yang, Shaohui Zhang, Qun Hao
https://arxiv.org/abs/2403.12970

Hybrid deep learning and physics-based neural network for programmable illumination computational microscopy
Relying on either deep models or physical models are two mainstream approaches for solving inverse sample reconstruction problems in programmable illumination computational microscopy. Solutions based on physical models possess strong generalization capabilities while struggling with global optimization of inverse problems due to a lack of insufficient physical constraints. In contrast, deep learning methods have strong problem-solving abilities, but their generalization ability is often questi…

Integer Programming Using A Single Atom
Kapil Goswami, Peter Schmelcher, Rick Mukherjee
https://arxiv.org/abs/2402.16541 https://arxi…

Integer Programming Using A Single Atom
Integer programming (IP), as the name suggests is an integer-variable-based approach commonly used to formulate real-world optimization problems with constraints. Currently, quantum algorithms reformulate the IP into an unconstrained form through the use of binary variables, which is an indirect and resource-consuming way of solving it. We develop an algorithm that maps and solves an IP problem in its original form to any quantum system that possesses a large number of accessible internal degre…

Leveraging Large Language Model to Generate a Novel Metaheuristic Algorithm with CRISPE Framework
Rui Zhong, Yuefeng Xu, Chao Zhang, Jun Yu
https://arxiv.org/abs/2403.16417

Leveraging Large Language Model to Generate a Novel Metaheuristic Algorithm with CRISPE Framework
In this paper, we borrow the large language model (LLM) ChatGPT-3.5 to automatically and quickly design a new metaheuristic algorithm (MA) with only a small amount of input. The novel animal-inspired MA named zoological search optimization (ZSO) draws inspiration from the collective behaviors of animals for solving continuous optimization problems. Specifically, the basic ZSO algorithm involves two search operators: the prey-predator interaction operator and the social flocking operator to bala…

A Uniform Framework for Language Inclusion Problems
Kyveli Doveri, Pierre Ganty, Chana Weil-Kennedy
https://arxiv.org/abs/2404.09862 https://

A Uniform Framework for Language Inclusion Problems
We present a uniform approach for solving language inclusion problems. Our approach relies on a least fixpoint characterization and a quasiorder to compare words of the "smaller" language, reducing the inclusion check to a finite number of membership queries in the "larger" language. We present our approach in detail on the case of inclusion of a context-free language given by a grammar into a regular language. We then explore other inclusion problems and discuss how to apply our approach.

About life and feelings, gloomy and private
The feelings we get from the activities we do could be classified as neutral, positive and negative.
Let's take developing #Gentoo as an example. It's something that makes me happy — but you can't (or at least I can't) just get the happiness and reject everything else. Most of the Gentoo work is basically neutral, even bland — a duty that takes a lot of time and effort, and probably a little of your health. It's statistically probable that you're going to get some positive feelings out of it — the joy of success, satisfaction, appreciation, awareness that you've done something good. But you also get negative feelings — from failures, frustration, negative interactions.
My hiking trips are like that too. My family believes that "I do it for pleasure" — but it's a harmful oversimplification and it only tells me that they even aren't trying to understand me. In fact, it's mostly a necessity, a way of solving specific problems that works for me — halting diabetes-related problems, coping with emotions. Of course there's a positive side to it — good mood, energy to survive another day, something the joy of visiting a new place, seeing something beautiful, finding a solution to a vexatious problem, positive interactions with people. But there are also negative feelings — anger and sadness from failure, stress from problems, negative contacts with people. Sometimes you end up slowly charging your social battery for a whole week, just to have one person destroy it all.
If you think about it, life's something like that. It's mostly a bland effort to survive every following day, sometimes interspersed with positive or negative moments.
#ActuallyAutistic

FMint: Bridging Human Designed and Data Pretrained Models for Differential Equation Foundation Model
Zezheng Song, Jiaxin Yuan, Haizhao Yang
https://arxiv.org/abs/2404.14688

FMint: Bridging Human Designed and Data Pretrained Models for Differential Equation Foundation Model
Human-designed algorithms have long been fundamental in solving a variety of scientific and engineering challenges. Recently, data-driven deep learning methods have also risen to prominence, offering innovative solutions across numerous scientific fields. While traditional algorithms excel in capturing the core aspects of specific problems, they often lack the flexibility needed for varying problem conditions due to the absence of specific data. Conversely, while data-driven approaches utilize …

This https://arxiv.org/abs/2311.17248 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_ees…

Deep Regularized Compound Gaussian Network for Solving Linear Inverse Problems
Incorporating prior information into inverse problems, e.g. via maximum-a-posteriori estimation, is an important technique for facilitating robust inverse problem solutions. In this paper, we devise two novel approaches for linear inverse problems that permit problem-specific statistical prior selections within the compound Gaussian (CG) class of distributions. The CG class subsumes many commonly used priors in signal and image reconstruction methods including those of sparsity-based approaches…

This https://arxiv.org/abs/2112.05645 has been replaced.
link: https://scholar.google.com/scholar?q=a

Graph-structured tensor optimization for nonlinear density control and mean field games
In this work we develop a numerical method for solving a type of convex graph-structured tensor optimization problems. This type of problems, which can be seen as a generalization of multi-marginal optimal transport problems with graph-structured costs, appear in many applications. Examples are unbalanced optimal transport and multi-species potential mean field games, where the latter is a class of nonlinear density control problems. The method we develop is based on coordinate ascent in a Lagr…

Gauge Theoretical Method in Solving Zero-curvature Equations I. -- Application to the Static Einstein-Maxwell Equations with Magnetic Charge
Takahiro Azuma (Dokkyo University), Takao Koikawa (Institute of Human Culture Studies, Otsuma Women's University)
https://arxiv.org/abs/2403.12375<…

Gauge Theoretical Method in Solving Zero-curvature Equations I. -- Application to the Static Einstein-Maxwell Equations with Magnetic Charge
The inverse scattering problem is applied to 2-dimensional partial differential equations called soliton equations such as the KdV equation and so on. It is also used to integrate the Einstein equations with axial symmetry. These inverse scattering problems look different. We show that they can be understood in a unified way. As an application to the Einstein equation, we find solutions of the Einstein-Maxwell equations with magnetic charge.

Lower bounds for quantum-inspired classical algorithms via communication complexity
Nikhil S. Mande, Changpeng Shao
https://arxiv.org/abs/2402.15686 https:…

Lower bounds for quantum-inspired classical algorithms via communication complexity
Quantum-inspired classical algorithms provide us with a new way to understand the computational power of quantum computers for practically-relevant problems, especially in machine learning. In the past several years, numerous efficient algorithms for various tasks have been found, while an analysis of lower bounds is still missing. Using communication complexity, in this work we propose the first method to study lower bounds for these tasks. We mainly focus on lower bounds for solving linear re…

MM-PhyRLHF: Reinforcement Learning Framework for Multimodal Physics Question-Answering
Avinash Anand, Janak Kapuriya, Chhavi Kirtani, Apoorv Singh, Jay Saraf, Naman Lal, Jatin Kumar, Adarsh Raj Shivam, Astha Verma, Rajiv Ratn Shah, Roger Zimmermann
https://arxiv.org/abs/2404.12926

MM-PhyRLHF: Reinforcement Learning Framework for Multimodal Physics Question-Answering
Recent advancements in LLMs have shown their significant potential in tasks like text summarization and generation. Yet, they often encounter difficulty while solving complex physics problems that require arithmetic calculation and a good understanding of concepts. Moreover, many physics problems include images that contain important details required to understand the problem's context. We propose an LMM-based chatbot to answer multimodal physics MCQs. For domain adaptation, we utilize the MM-P…

Generalized Multiscale Finite Element Method for discrete network (graph) models
Maria Vasilyeva
https://arxiv.org/abs/2404.16554 https://

Generalized Multiscale Finite Element Method for discrete network (graph) models
In this paper, we consider a time-dependent discrete network model with highly varying connectivity. The approximation by time is performed using an implicit scheme. We propose the coarse scale approximation construction of network models based on the Generalized Multiscale Finite Element Method. An accurate coarse-scale approximation is generated by solving local spectral problems in sub-networks. Convergence analysis of the proposed method is presented for semi-discrete and discrete network m…

Lower bounds for quantum-inspired classical algorithms via communication complexity
Nikhil S. Mande, Changpeng Shao
https://arxiv.org/abs/2402.15686 https:…

Lower bounds for quantum-inspired classical algorithms via communication complexity
Quantum-inspired classical algorithms provide us with a new way to understand the computational power of quantum computers for practically-relevant problems, especially in machine learning. In the past several years, numerous efficient algorithms for various tasks have been found, while an analysis of lower bounds is still missing. Using communication complexity, in this work we propose the first method to study lower bounds for these tasks. We mainly focus on lower bounds for solving linear re…

if you set two dozen people on solving the environmental problems we face,
and they each focused on different things,
would their different solutions be harmonious? like a "yes, and"?
e.g. are all straightforward, cost effective, solutions we can do now... non-conflicting?
like swapping to alternatives for milk / not shipping water around,
or meat, or air travel,
swapping to EVs for rural america and improving trains to replace highways/flying, a cleaner grid but also the battery recycling,
swapping to nuclear, wind, and solar, dealing with recycling all of them in stride
supply chain plastics, single use plastics,
not using massive AI datacenters to do that stuff
changes in lobbying, taxes, subsidies, regulations,
if you had 24 people - would their ideas be synergistic? #ClimateChange #GreenEnergy

Optimal schedules for annealing algorithms
Amin Barzegar, Firas Hamze, Christopher Amey, Jonathan Machta
https://arxiv.org/abs/2402.14717 https://

Optimal schedules for annealing algorithms
Annealing algorithms such as simulated annealing and population annealing are widely used both for sampling the Gibbs distribution and solving optimization problems (i.e. finding ground states). For both statistical mechanics and optimization, additional parameters beyond temperature are often needed such as chemical potentials, external fields or Lagrange multipliers enforcing constraints. In this paper we derive a formalism for optimal annealing schedules in multidimensional parameter spaces …

Get fun ideas for coding and robotics in grades K-8, like making games, creating stories, programming robots, and solving problems! https://blog.tcea.org/scope-and-sequence-computational-thinking-part-2/

This https://arxiv.org/abs/2401.02873 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Optimal Chaining of Vehicle Plans with Time Windows
For solving problems from the domain of Mobility-on-Demand (MoD), we often need to connect vehicle plans into plans spanning longer time, a process we call plan chaining. As we show in this work, chaining of the plans can be used to reduce the size of MoD providers' fleet (fleet-sizing problem) but also to reduce the total driven distance by providing high-quality vehicle dispatching solutions in MoD systems. Recently, a solution that uses this principle has been proposed to solve the fleet-siz…

Trigonometry and Analytic Tools in Olympiad Geometry Problems, Part I
Orestis Lignos
https://arxiv.org/abs/2403.09661 https://arxiv.o…

Trigonometry and Analytic Tools in Olympiad Geometry Problems, Part I
This is the first part of a series of papers aiming to show how trigonometry and analytic tools can help into tackling demanding Olympiad geometry problems. We present several novel techniques for tackling hard problems from various international and national mathematical competitions, and develop the appropriate theoretical background. Several insightful examples and practice problems are included for the reader to sharpen their problem solving skills. The number of asterisks next to each pr…

As I came of age in the mid 70s, I "learned" that the markets drove innovation and provided solutions - while government was "the problem". WHen I look at utilities I see the opposite - rent seeking, and a failure to copy - not even invest in R&D, just copy - demonstrated solutions to problems. Maybe we need to rethink the role of private utilities? Because they seen incapable of solving the critical problems we face, while charging more and more to replace infras…

The U.S. Urgently Needs a Bigger Grid. Here’s a Fast Solution.
A rarely used technique to upgrade old power lines could play a big role in fixing one of the largest obstacles facing clean energy, two reports found.

As I came of age in the mid 70s, I "learned" that the markets drove innovation and provided solutions - while government was "the problem". WHen I look at utilities I see the opposite - rent seeking, and a failure to copy - not even invest in R&D, just copy - demonstrated solutions to problems. Maybe we need to rethink the role of private utilities? Because they seen incapable of solving the critical problems we face, while charging more and more to replace infras…

The U.S. Urgently Needs a Bigger Grid. Here’s a Fast Solution.
A rarely used technique to upgrade old power lines could play a big role in fixing one of the largest obstacles facing clean energy, two reports found.

Solving the Gibbs Problem with Algebraic Projective Geometry
Michela Mancini, John A. Christian
https://arxiv.org/abs/2403.08893 https://

Solving the Gibbs Problem with Algebraic Projective Geometry
Orbit determination (OD) from three position vectors is one of the classical problems in astrodynamics. Early contributions to this problem were made by J. Willard Gibbs in the late 1800s and OD of this type is known today as ``Gibbs Problem''. There are a variety of popular solutions to the Gibbs problem. While some authors solve for the orbital elements directly, most contemporary discussions are based on a vector analysis approach inspired by Gibbs himself. This work presents a completely …

This https://arxiv.org/abs/2312.17471 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_ees…

Solving Decision-Dependent Games by Learning from Feedback
This paper tackles the problem of solving stochastic optimization problems with a decision-dependent distribution in the setting of stochastic strongly-monotone games and when the distributional dependence is unknown. A two-stage approach is proposed, which initially involves estimating the distributional dependence on decision variables, and subsequently optimizing over the estimated distributional map. The paper presents guarantees for the approximation of the cost of each agent. Furthermore,…

Small successes - solving one of last week's problems by setting client's timeout back to old defaults after missing upstream documented change as non-applicable for this problem. *sigh*
#complexity #CodeLiability

Robust mass lumping and outlier removal strategies in isogeometric analysis
Yannis Voet, Espen Sande, Annalisa Buffa
https://arxiv.org/abs/2402.14956 https…

Robust mass lumping and outlier removal strategies in isogeometric analysis
Mass lumping techniques are commonly employed in explicit time integration schemes for problems in structural dynamics and both avoid solving costly linear systems with the consistent mass matrix and increase the critical time step. In isogeometric analysis, the critical time step is constrained by so-called "outlier" frequencies, representing the inaccurate high frequency part of the spectrum. Removing or dampening these high frequencies is paramount for fast explicit solution techniques. In t…

This https://arxiv.org/abs/2403.09133 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

A Low-Rank ADMM Splitting Approach for Semidefinite Programming
We introduce a new first-order method for solving general semidefinite programming problems, based on the alternating direction method of multipliers (ADMM) and a matrix-splitting technique. Our algorithm has an advantage over the Burer-Monteiro approach as it only involves much easier quadratically regularized subproblems in each iteration. For a linear objective, the subproblems are well-conditioned quadratic programs that can be efficiently solved by the standard conjugate gradient method. W…

Robustness and Exploration of Variational and Machine Learning Approaches to Inverse Problems: An Overview
Alexander Auras, Kanchana Vaishnavi Gandikota, Hannah Droege, Michael Moeller
https://arxiv.org/abs/2402.12072

Robustness and Exploration of Variational and Machine Learning Approaches to Inverse Problems: An Overview
This paper attempts to provide an overview of current approaches for solving inverse problems in imaging using variational methods and machine learning. A special focus lies on point estimators and their robustness against adversarial perturbations. In this context results of numerical experiments for a one-dimensional toy problem are provided, showing the robustness of different approaches and empirically verifying theoretical guarantees. Another focus of this review is the exploration of the …

A new approach for solving global optimization and engineering problems based on modified Sea Horse Optimizer
Fatma A. Hashim, Reham R. Mostafa, Ruba Abu Khurma, Raneem Qaddoura, P. A. Castillo
https://arxiv.org/abs/2402.14044 https://arxiv.org/pdf/2402.14044
arXiv:2402.14044v1 Announce Type: new
Abstract: Sea Horse Optimizer (SHO) is a noteworthy metaheuristic algorithm that emulates various intelligent behaviors exhibited by sea horses, encompassing feeding patterns, male reproductive strategies, and intricate movement patterns. To mimic the nuanced locomotion of sea horses, SHO integrates the logarithmic helical equation and Levy flight, effectively incorporating both random movements with substantial step sizes and refined local exploitation. Additionally, the utilization of Brownian motion facilitates a more comprehensive exploration of the search space. This study introduces a robust and high-performance variant of the SHO algorithm named mSHO. The enhancement primarily focuses on bolstering SHO's exploitation capabilities by replacing its original method with an innovative local search strategy encompassing three distinct steps: a neighborhood-based local search, a global non-neighbor-based search, and a method involving circumnavigation of the existing search region. These techniques improve mSHO algorithm's search capabilities, allowing it to navigate the search space and converge toward optimal solutions efficiently. The comprehensive results distinctly establish the supremacy and efficiency of the mSHO method as an exemplary tool for tackling an array of optimization quandaries. The results show that the proposed mSHO algorithm has a total rank of 1 for CEC'2020 test functions. In contrast, the mSHO achieved the best value for the engineering problems, recording a value of 0.012665, 2993.634, 0.01266, 1.724967, 263.8915, 0.032255, 58507.14, 1.339956, and 0.23524 for the pressure vessel design, speed reducer design, tension/compression spring, welded beam design, three-bar truss engineering design, industrial refrigeration system, multi-Product batch plant, cantilever beam problem, multiple disc clutch brake problems, respectively.

Quantum computing in civil engineering: Limitations
Joern Ploennigs, Markus Berger, Martin Mevissen, Kay Smarsly
https://arxiv.org/abs/2402.14556 https://<…

Quantum computing in civil engineering: Limitations
Quantum computing is a new computational paradigm with the potential to solve certain computationally challenging problems much faster than traditional approaches. Civil engineering encompasses many computationally challenging problems, which leads to the question of how well quantum computing is suitable for solving civil engineering problems and how much impact and implications to the field of civil engineering can be expected when deploying quantum computing for solving these problems. To ad…

SAAS: Solving Ability Amplification Strategy for Enhanced Mathematical Reasoning in Large Language Models
Hyeonwoo Kim, Gyoungjin Gim, Yungi Kim, Jihoo Kim, Byungju Kim, Wonseok Lee, Chanjun Park
https://arxiv.org/abs/2404.03887

SAAS: Solving Ability Amplification Strategy for Enhanced Mathematical Reasoning in Large Language Models
This study presents a novel learning approach designed to enhance both mathematical reasoning and problem-solving abilities of Large Language Models (LLMs). We focus on integrating the Chain-of-Thought (CoT) and the Program-of-Thought (PoT) learning, hypothesizing that prioritizing the learning of mathematical reasoning ability is helpful for the amplification of problem-solving ability. Thus, the initial learning with CoT is essential for solving challenging mathematical problems. To this end,…

This https://arxiv.org/abs/2311.17248 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_ees…

Deep Regularized Compound Gaussian Network for Solving Linear Inverse Problems
Incorporating prior information into inverse problems, e.g. via maximum-a-posteriori estimation, is an important technique for facilitating robust inverse problem solutions. In this paper, we devise two novel approaches for linear inverse problems that permit problem-specific statistical prior selections within the compound Gaussian (CG) class of distributions. The CG class subsumes many commonly used priors in signal and image reconstruction methods including those of sparsity-based approaches…

GeoEval: Benchmark for Evaluating LLMs and Multi-Modal Models on Geometry Problem-Solving
Jiaxin Zhang, Zhongzhi Li, Mingliang Zhang, Fei Yin, Chenglin Liu, Yashar Moshfeghi
https://arxiv.org/abs/2402.10104

GeoEval: Benchmark for Evaluating LLMs and Multi-Modal Models on Geometry Problem-Solving
Recent advancements in Large Language Models (LLMs) and Multi-Modal Models (MMs) have demonstrated their remarkable capabilities in problem-solving. Yet, their proficiency in tackling geometry math problems, which necessitates an integrated understanding of both textual and visual information, has not been thoroughly evaluated. To address this gap, we introduce the GeoEval benchmark, a comprehensive collection that includes a main subset of 2000 problems, a 750 problem subset focusing on backwa…

A new approach for solving global optimization and engineering problems based on modified Sea Horse Optimizer
Fatma A. Hashim, Reham R. Mostafa, Ruba Abu Khurma, Raneem Qaddoura, P. A. Castillo
https://arxiv.org/abs/2402.14044 https://arxiv.org/pdf/2402.14044
arXiv:2402.14044v1 Announce Type: new
Abstract: Sea Horse Optimizer (SHO) is a noteworthy metaheuristic algorithm that emulates various intelligent behaviors exhibited by sea horses, encompassing feeding patterns, male reproductive strategies, and intricate movement patterns. To mimic the nuanced locomotion of sea horses, SHO integrates the logarithmic helical equation and Levy flight, effectively incorporating both random movements with substantial step sizes and refined local exploitation. Additionally, the utilization of Brownian motion facilitates a more comprehensive exploration of the search space. This study introduces a robust and high-performance variant of the SHO algorithm named mSHO. The enhancement primarily focuses on bolstering SHO's exploitation capabilities by replacing its original method with an innovative local search strategy encompassing three distinct steps: a neighborhood-based local search, a global non-neighbor-based search, and a method involving circumnavigation of the existing search region. These techniques improve mSHO algorithm's search capabilities, allowing it to navigate the search space and converge toward optimal solutions efficiently. The comprehensive results distinctly establish the supremacy and efficiency of the mSHO method as an exemplary tool for tackling an array of optimization quandaries. The results show that the proposed mSHO algorithm has a total rank of 1 for CEC'2020 test functions. In contrast, the mSHO achieved the best value for the engineering problems, recording a value of 0.012665, 2993.634, 0.01266, 1.724967, 263.8915, 0.032255, 58507.14, 1.339956, and 0.23524 for the pressure vessel design, speed reducer design, tension/compression spring, welded beam design, three-bar truss engineering design, industrial refrigeration system, multi-Product batch plant, cantilever beam problem, multiple disc clutch brake problems, respectively.

TENG: Time-Evolving Natural Gradient for Solving PDEs with Deep Neural Net
Zhuo Chen, Jacob McCarran, Esteban Vizcaino, Marin Solja\v{c}i\'c, Di Luo
https://arxiv.org/abs/2404.10771

TENG: Time-Evolving Natural Gradient for Solving PDEs with Deep Neural Net
Partial differential equations (PDEs) are instrumental for modeling dynamical systems in science and engineering. The advent of neural networks has initiated a significant shift in tackling these complexities though challenges in accuracy persist, especially for initial value problems. In this paper, we introduce the $\textit{Time-Evolving Natural Gradient (TENG)}$, generalizing time-dependent variational principles and optimization-based time integration, leveraging natural gradient optimizati…

Dionysos.jl: a Modular Platform for Smart Symbolic Control
Julien Calbert, Adrien Banse, Beno\^it Legat, Rapha\"el M. Jungers
https://arxiv.org/abs/2404.14114

Dionysos.jl: a Modular Platform for Smart Symbolic Control
We introduce Dionysos.jl, a modular package for solving optimal control problems for complex dynamical systems using state-of-the-art and experimental techniques from symbolic control, optimization, and learning. More often than not with Cyber-Physical systems, the only sensible way of developing a controller is by discretizing the different variables, thus transforming the control task into a purely combinatorial problem on a finite-state mathematical object, called an abstraction of this syst…

This https://arxiv.org/abs/2303.14971 has been replaced.
link: https://scholar.google.com/scholar?q=a

On CNF Conversion for SAT and SMT Enumeration
Modern SAT and SMT solvers are designed to handle problems expressed in Conjunctive Normal Form (CNF) so that non-CNF problems must be CNF-ized upfront, typically by using variants of either Tseitin or Plaisted and Greenbaum transformations. When passing from solving to enumeration, however, the capability of producing partial satisfying assignments that are as small as possible becomes crucial, which raises the question of whether such CNF encodings are also effective for enumeration. In thi…

Small successes - solving one of last week's problems by setting client's timeout back to old defaults after missing upstream documented change as non-applicable for this problem. *sigh*
#complexity #CodeLiability

This https://arxiv.org/abs/2310.09844 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Risk-Adaptive Local Decision Rules
For parameterized mixed-binary optimization problems, we construct local decision rules that prescribe near-optimal courses of action across a set of parameter values. The decision rules stem from solving risk-adaptive training problems over classes of continuous, possibly nonlinear mappings. In asymptotic and nonasymptotic analysis, we establish that the decision rules prescribe near-optimal decisions locally for the actual problems, without relying on linearity, convexity, or smoothness. The …

Hybrid Quantum Tabu Search for Solving the Vehicle Routing Problem
James Holliday, Braeden Morgan, Hugh Churchill, Khoa Luu
https://arxiv.org/abs/2404.13203

Hybrid Quantum Tabu Search for Solving the Vehicle Routing Problem
There has never been a more exciting time for the future of quantum computing than now. Near-term quantum computing usage is now the next XPRIZE. With that challenge in mind we have explored a new approach as a hybrid quantum-classical algorithm for solving NP-Hard optimization problems. We have focused on the classic problem of the Capacitated Vehicle Routing Problem (CVRP) because of its real-world industry applications. Heuristics are often employed to solve this problem because it is diffic…

This https://arxiv.org/abs/2307.10635 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csCL_…

SciBench: Evaluating College-Level Scientific Problem-Solving Abilities of Large Language Models
Most of the existing Large Language Model (LLM) benchmarks on scientific problem reasoning focus on problems grounded in high-school subjects and are confined to elementary algebraic operations. To systematically examine the reasoning capabilities required for solving complex scientific problems, we introduce an expansive benchmark suite SciBench for LLMs. SciBench contains a carefully curated dataset featuring a range of collegiate-level scientific problems from mathematics, chemistry, and phy…

This https://arxiv.org/abs/2305.17799 has been replaced.
link: https://scholar.google.com/scholar?q=a

I-FENN for thermoelasticity based on physics-informed temporal convolutional network (PI-TCN)
Most currently available methods for modeling multiphysics, including thermoelasticity, using machine learning approaches, are focused on solving complete multiphysics problems using data-driven or physics-informed multi-layer perceptron (MLP) networks. Such models rely on incremental step-wise training of the MLPs, and lead to elevated computational expense; they also lack the rigor of existing numerical methods like the finite element method. We propose an integrated finite element neural net…

Anderson Acceleration with Truncated Gram-Schmidt
Ziyuan Tang, Tianshi Xu, Huan He, Yousef Saad, Yuanzhe Xi
https://arxiv.org/abs/2403.14961 https://

Anderson Acceleration with Truncated Gram-Schmidt
Anderson Acceleration (AA) is a popular algorithm designed to enhance the convergence of fixed-point iterations. In this paper, we introduce a variant of AA based on a Truncated Gram-Schmidt process (AATGS) which has a few advantages over the classical AA. In particular, an attractive feature of AATGS is that its iterates obey a three-term recurrence in the situation when it is applied to solving symmetric linear problems and this can lead to a considerable reduction of memory and computational…

QSMDiff: Unsupervised 3D Diffusion Models for Quantitative Susceptibility Mapping
Zhuang Xiong, Wei Jiang, Yang Gao, Feng Liu, Hongfu Sun
https://arxiv.org/abs/2403.14070

QSMDiff: Unsupervised 3D Diffusion Models for Quantitative Susceptibility Mapping
Quantitative Susceptibility Mapping (QSM) dipole inversion is an ill-posed inverse problem for quantifying magnetic susceptibility distributions from MRI tissue phases. While supervised deep learning methods have shown success in specific QSM tasks, their generalizability across different acquisition scenarios remains constrained. Recent developments in diffusion models have demonstrated potential for solving 2D medical imaging inverse problems. However, their application to 3D modalities, such…

MACM: Utilizing a Multi-Agent System for Condition Mining in Solving Complex Mathematical Problems
Bin Lei
https://arxiv.org/abs/2404.04735 https://…

MACM: Utilizing a Multi-Agent System for Condition Mining in Solving Complex Mathematical Problems
Recent advancements in large language models, such as GPT-4, have demonstrated remarkable capabilities in processing standard queries. Despite these advancements, their performance substantially declines in \textbf{advanced mathematical problems requiring complex, multi-step logical reasoning}. To enhance their inferential capabilities, current research has delved into \textit{prompting engineering}, exemplified by methodologies such as the Tree of Thought and Graph of Thought. Nonetheless, the…

Anderson acceleration of derivative-free projection methods for constrained monotone nonlinear equations
Jiachen Jin, Hongxia Wang, Kangkang Deng
https://arxiv.org/abs/2403.14924 …

Anderson acceleration of derivative-free projection methods for constrained monotone nonlinear equations
The derivative-free projection method (DFPM) is an efficient algorithm for solving monotone nonlinear equations. As problems grow larger, there is a strong demand for speeding up the convergence of DFPM. This paper considers the application of Anderson acceleration (AA) to DFPM for constrained monotone nonlinear equations. By employing a nonstationary relaxation parameter and interleaving with slight modifications in each iteration, a globally convergent variant of AA for DFPM named as AA-DFPM …

This https://arxiv.org/abs/2307.10635 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csCL_…

SciBench: Evaluating College-Level Scientific Problem-Solving Abilities of Large Language Models
Most of the existing Large Language Model (LLM) benchmarks on scientific problem reasoning focus on problems grounded in high-school subjects and are confined to elementary algebraic operations. To systematically examine the reasoning capabilities required for solving complex scientific problems, we introduce an expansive benchmark suite SciBench for LLMs. SciBench contains a carefully curated dataset featuring a range of collegiate-level scientific problems from mathematics, chemistry, and phy…

Solving fluid flow problems in space-time with multiscale stabilization: formulation and examples
Biswajit Khara, Robert Dyja, Kumar Saurabh, Anupam Sharma, Baskar Ganapathysubramanian
https://arxiv.org/abs/2402.12571

Solving fluid flow problems in space-time with multiscale stabilization: formulation and examples
We solve fluid flow problems through a space-time finite element method. The weak form of the Navier-Stokes equations is stabilized using the variational multi-scale formulation. The finite element problem is posed on the "full" space-time domain, considering time as another dimension. We apply this method on two benchmark problems in computational fluid dynamics, namely, lid-driven cavity flow and flow past a circular cylinder. We validate the current method with existing results from literatu…

Synthesizing Controller for Safe Navigation using Control Density Function
Joseph Moyalan, Sriram S. K. S Narayanan, Andrew Zheng, Umesh Vaidya
https://arxiv.org/abs/2403.14464

Synthesizing Controller for Safe Navigation using Control Density Function
We consider the problem of navigating a nonlinear dynamical system from some initial set to some target set while avoiding collision with an unsafe set. We extend the concept of density function to control density function (CDF) for solving navigation problems with safety constraints. The occupancy-based interpretation of the measure associated with the density function is instrumental in imposing the safety constraints. The navigation problem with safety constraints is formulated as a quadrati…

Variable Projection Algorithms: Theoretical Insights and A Novel Approach for Problems with Large Residual
Guangyong Chen, Peng Xue, Min Gan, Jing Chen, Wenzhong Guo, C. L. Philip. Chen
https://arxiv.org/abs/2402.13865

Variable Projection Algorithms: Theoretical Insights and A Novel Approach for Problems with Large Residual
This paper delves into an in-depth exploration of the Variable Projection (VP) algorithm, a powerful tool for solving separable nonlinear optimization problems across multiple domains, including system identification, image processing, and machine learning. We first establish a theoretical framework to examine the effect of the approximate treatment of the coupling relationship among parameters on the local convergence of the VP algorithm and theoretically prove that the Kaufman's VP algorithm …

Bridging the Gap Between Theory and Practice: Benchmarking Transfer Evolutionary Optimization
Yaqing Hou, Wenqiang Ma, Abhishek Gupta, Kavitesh Kumar Bali, Hongwei Ge, Qiang Zhang, Carlos A. Coello Coello, Yew-Soon Ong
https://arxiv.org/abs/2404.13377

Bridging the Gap Between Theory and Practice: Benchmarking Transfer Evolutionary Optimization
In recent years, the field of Transfer Evolutionary Optimization (TrEO) has witnessed substantial growth, fueled by the realization of its profound impact on solving complex problems. Numerous algorithms have emerged to address the challenges posed by transferring knowledge between tasks. However, the recently highlighted ``no free lunch theorem'' in transfer optimization clarifies that no single algorithm reigns supreme across diverse problem types. This paper addresses this conundrum by adopt…

A preconditioner for solving linear programming problems with dense columns
Catalina J. Villalba, Aurelio R. L. Oliveira
https://arxiv.org/abs/2404.10930 h…

A preconditioner for solving linear programming problems with dense columns
The Interior-Point Methods are a class for solving linear programming problems that rely upon the solution of linear systems. At each iteration, it becomes important to determine how to solve these linear systems when the constraint matrix of the linear programming problem includes dense columns. In this paper, we propose a preconditioner to handle linear programming problems with dense columns, and we prove theoretically that the final linear system to solve is uniformly bounded when the Inter…

Numerical Discretization Methods for Linear Quadratic Control Problems with Time Delays
Zhanhao Zhang, Steen H{\o}rsholt, John Bagterp J{\o}rgensen
https://arxiv.org/abs/2404.08440

Numerical Discretization Methods for Linear Quadratic Control Problems with Time Delays
This paper presents the numerical discretization methods of the continuous-time linear-quadratic optimal control problems (LQ-OCPs) with time delays. We describe the weight matrices of the LQ-OCPs as differential equations systems, allowing us to derive the discrete equivalent of the continuous-time LQ-OCPs. Three numerical methods are introduced for solving proposed differential equations systems: 1) the ordinary differential equation (ODE) method, 2) the matrix exponential method, and 3) the …

This https://arxiv.org/abs/2308.07812 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

An efficient sieving based secant method for sparse optimization problems with least-squares constraints
In this paper, we propose an efficient sieving based secant method to address the computational challenges of solving sparse optimization problems with least-squares constraints. A level-set method has been introduced in [X. Li, D.F. Sun, and K.-C. Toh, SIAM J. Optim., 28 (2018), pp. 1842--1866] that solves these problems by using the bisection method to find a root of a univariate nonsmooth equation $φ(λ) = \varrho$ for some $\varrho > 0$, where $φ(\cdot)$ is the value function computed by …

An inexact augmented Lagrangian algorithm for unsymmetric saddle-point systems
N. Huang, Y. -H. Dai, D. Orban, M. A. Saunders
https://arxiv.org/abs/2404.14636

An inexact augmented Lagrangian algorithm for unsymmetric saddle-point systems
Augmented Lagrangian (AL) methods are a well known class of algorithms for solving constrained optimization problems. They have been extended to the solution of saddle-point systems of linear equations. We study an AL (SPAL) algorithm for unsymmetric saddle-point systems and derive convergence and semi-convergence properties, even when the system is singular. At each step, our SPAL requires the exact solution of a linear system of the same size but with an SPD (2,2) block. To improve efficiency…

Data Augmentation with In-Context Learning and Comparative Evaluation in Math Word Problem Solving
Gulsum Yigit, Mehmet Fatih Amasyali
https://arxiv.org/abs/2404.03938

Data Augmentation with In-Context Learning and Comparative Evaluation in Math Word Problem Solving
Math Word Problem (MWP) solving presents a challenging task in Natural Language Processing (NLP). This study aims to provide MWP solvers with a more diverse training set, ultimately improving their ability to solve various math problems. We propose several methods for data augmentation by modifying the problem texts and equations, such as synonym replacement, rule-based: question replacement, and rule based: reversing question methodologies over two English MWP datasets. This study extends by i…

This https://arxiv.org/abs/2212.11336 has been replaced.
link: https://scholar.google.com/scholar?q=a

An inertial ADMM for a class of nonconvex composite optimization with nonlinear coupling constraints
In this paper, we propose an inertial alternating direction method of multipliers for solving a class of non-convex multi-block optimization problems with \emph{nonlinear coupling constraints}. Distinctive features of our proposed method, when compared with other alternating direction methods of multipliers for solving non-convex problems with nonlinear coupling constraints, include: (i) we apply the inertial technique to the update of primal variables and (ii) we apply a non-standard update ru…

This https://arxiv.org/abs/2402.07064 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Exact Semi-Definite Programs for Piecewise SOS-Convex Moment Optimization and Applications
In this paper, we present exact Semi-Definite Program (SDP) reformulations for a broad class of infinite-dimensional moment optimization problems involving piecewise Sums-of-Squares (SOS) convex polynomials and projected spectrahedral support sets. These reformulations show that the optimal value of the original moment problem can be found by solving a single SDP. In particular, we show how an optimal probability measure is recovered for these problems by solving a single SDP. This is done by f…

Learning from Offline and Online Experiences: A Hybrid Adaptive Operator Selection Framework
Jiyuan Pei, Jialin Liu, Yi Mei
https://arxiv.org/abs/2404.10252

Learning from Offline and Online Experiences: A Hybrid Adaptive Operator Selection Framework
In many practical applications, usually, similar optimisation problems or scenarios repeatedly appear. Learning from previous problem-solving experiences can help adjust algorithm components of meta-heuristics, e.g., adaptively selecting promising search operators, to achieve better optimisation performance. However, those experiences obtained from previously solved problems, namely offline experiences, may sometimes provide misleading perceptions when solving a new problem, if the characterist…

This https://arxiv.org/abs/2403.16698 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_qu…

Boson sampling enhanced quantum chemistry
In this work, we give a hybrid quantum-classical algorithm for solving electronic structure problems of molecules using only linear quantum optical systems. The variational ansatz we proposed is a hybrid of non-interacting Boson dynamics and classical computational chemistry methods, specifically, the Hartree-Fock method and the Configuration Interaction method. The Boson part is built by a linear optical interferometer which is easier to realize compared with the well-known Unitary Coupled Clu…

This https://arxiv.org/abs/2311.12528 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Inverse Problems with Learned Forward Operators
Solving inverse problems requires the knowledge of the forward operator, but accurate models can be computationally expensive and hence cheaper variants that do not compromise the reconstruction quality are desired. This chapter reviews reconstruction methods in inverse problems with learned forward operators that follow two different paradigms. The first one is completely agnostic to the forward operator and learns its restriction to the subspace spanned by the training data. The framework of …

Solving Combinatorial Pricing Problems using Embedded Dynamic Programming Models
Quang Minh Bui, Margarida Carvalho, Jos\'e Neto
https://arxiv.org/abs/2403.12923

Solving Combinatorial Pricing Problems using Embedded Dynamic Programming Models
The combinatorial pricing problem (CPP) is a bilevel problem in which the leader maximizes their revenue by imposing tolls on certain items that they can control. Based on the tolls set by the leader, the follower selects a subset of items corresponding to an optimal solution of a combinatorial optimization problem. To accomplish the leader's goal, the tolls need to be sufficiently low to discourage the follower from choosing the items offered by the competitors. In this paper, we derive a sing…

This https://arxiv.org/abs/2111.08108 has been replaced.
link: https://scholar.google.com/scholar?q=a

Learning Optimal Control with Stochastic Models of Hamiltonian Dynamics
Optimal control problems can be solved by applying the Pontryagin maximum principle and then solving for a Hamiltonian dynamical system. In this paper, we propose novel learning frameworks to tackle optimal control problems. By applying the Pontryagin maximum principle to the original optimal control problem, the learning focus shifts to reduced Hamiltonian dynamics and corresponding adjoint variables. The reduced Hamiltonian networks can be learned by going backward in time and then minimizing…

Two trust region type algorithms for solving nonconvex-strongly concave minimax problems
Tongliang Yao, Zi Xu
https://arxiv.org/abs/2402.09807 https://

Two trust region type algorithms for solving nonconvex-strongly concave minimax problems
In this paper, we propose a Minimax Trust Region (MINIMAX-TR) algorithm and a Minimax Trust Region Algorithm with Contractions and Expansions(MINIMAX-TRACE) algorithm for solving nonconvex-strongly concave minimax problems. Both algorithms can find an $(ε, \sqrtε)$-second order stationary point(SSP) within $\mathcal{O}(ε^{-1.5})$ iterations, which matches the best well known iteration complexity.

Robust SGLD algorithm for solving non-convex distributionally robust optimisation problems
Ariel Neufeld, Matthew Ng Cheng En, Ying Zhang
https://arxiv.org/abs/2403.09532

Robust SGLD algorithm for solving non-convex distributionally robust optimisation problems
In this paper we develop a Stochastic Gradient Langevin Dynamics (SGLD) algorithm tailored for solving a certain class of non-convex distributionally robust optimisation problems. By deriving non-asymptotic convergence bounds, we build an algorithm which for any prescribed accuracy $\varepsilon>0$ outputs an estimator whose expected excess risk is at most $\varepsilon$. As a concrete application, we employ our robust SGLD algorithm to solve the (regularised) distributionally robust Mean-CVaR po…

Tikhonov regularized exterior penalty dynamics for constrained variational inequalities
Siqi Qu, Mathias Staudigl
https://arxiv.org/abs/2403.13460 https://…

Tikhonov regularized exterior penalty dynamics for constrained variational inequalities
Solving equilibrium problems under constraints is an important problem in optimization and optimal control. In this context an important practical challenge is the efficient incorporation of constraints. We develop a continuous-time method for solving constrained variational inequalities based on a new penalty regulated dynamical system in a general potentially infinite-dimensional Hilbert space. In order to obtain strong convergence of the issued trajectory of our method, we incorporate an exp…

This https://arxiv.org/abs/2205.10969 has been replaced.
link: https://scholar.google.com/scholar?q=a

Application of tropical optimization for solving multicriteria problems of pairwise comparisons using log-Chebyshev approximation
We consider a decision-making problem to find absolute ratings of alternatives that are compared in pairs under multiple criteria, subject to constraints in the form of two-sided bounds on ratios between the ratings. Given matrices of pairwise comparisons made according to the criteria, the problem is formulated as the log-Chebyshev approximation of these matrices by a common consistent matrix (a symmetrically reciprocal matrix of unit rank) to minimize the approximation errors for all matrices…

This https://arxiv.org/abs/2304.02338 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Solving decision problems with endogenous uncertainty and conditional information revelation using influence diagrams
Despite methodological advances for modeling decision problems under uncertainty, representing endogenous uncertainty still proves challenging both in terms of modeling capabilities and computational requirements. A novel reformulation based on rooted junction trees (RJTs) provides an approach for solving such decision problems using off-the-shelf mathematical optimization solvers. This is made possible by using influence diagrams to represent a given decision problem and reformulating them as …

This https://arxiv.org/abs/2203.11329 has been replaced.
link: https://scholar.google.com/scholar?q=a

A model-free approach for solving choice-based competitive facility location problems using simulation and submodularity
This paper considers facility location problems in which a firm entering a market seeks to open facilities on a subset of candidate locations so as to maximize its expected market share, assuming that customers choose the available alternative that maximizes a random utility function. We introduce a deterministic equivalent reformulation of this stochastic problem as a maximum covering location problem with an exponential number of demand points, each of which is covered by a different set of c…

A Stochastic GDA Method With Backtracking For Solving Nonconvex (Strongly) Concave Minimax Problems
Qiushui Xu, Xuan Zhang, Necdet Serhat Aybat, Mert G\"urb\"uzbalaban
https://arxiv.org/abs/2403.07806

A Stochastic GDA Method With Backtracking For Solving Nonconvex (Strongly) Concave Minimax Problems
We propose a stochastic GDA (gradient descent ascent) method with backtracking (SGDA-B) to solve nonconvex-(strongly) concave (NCC) minimax problems $\min_x \max_y \sum_{i=1}^N g_i(x_i)+f(x,y)-h(y)$, where $h$ and $g_i$ for $i = 1, \ldots, N$ are closed, convex functions, $f$ is $L$-smooth and $μ$-strongly concave in $y$ for some $μ\geq 0$. We consider two scenarios: (i) the deterministic setting where we assume one can compute $\nabla f$ exactly, and (ii) the stochastic setting where we have…

A Stochastic GDA Method With Backtracking For Solving Nonconvex (Strongly) Concave Minimax Problems
Qiushui Xu, Xuan Zhang, Necdet Serhat Aybat, Mert G\"urb\"uzbalaban
https://arxiv.org/abs/2403.07806

A Stochastic GDA Method With Backtracking For Solving Nonconvex (Strongly) Concave Minimax Problems
We propose a stochastic GDA (gradient descent ascent) method with backtracking (SGDA-B) to solve nonconvex-(strongly) concave (NCC) minimax problems $\min_x \max_y \sum_{i=1}^N g_i(x_i)+f(x,y)-h(y)$, where $h$ and $g_i$ for $i = 1, \ldots, N$ are closed, convex functions, $f$ is $L$-smooth and $μ$-strongly concave in $y$ for some $μ\geq 0$. We consider two scenarios: (i) the deterministic setting where we assume one can compute $\nabla f$ exactly, and (ii) the stochastic setting where we have…

Derivative-Free Optimization via Adaptive Sampling Strategies
Raghu Bollapragada, Cem Karamanli, Stefan M. Wild
https://arxiv.org/abs/2404.11893 https://…

Derivative-Free Optimization via Adaptive Sampling Strategies
In this paper, we present a novel derivative-free optimization framework for solving unconstrained stochastic optimization problems. Many problems in fields ranging from simulation optimization to reinforcement learning involve settings where only stochastic function values are obtained via an oracle with no available gradient information, necessitating the usage of derivative-free optimization methodologies. Our approach includes estimating gradients using stochastic function evaluations and i…

This https://arxiv.org/abs/2310.04345 has been replaced.
link: https://scholar.google.com/scholar?q=a

Neur2RO: Neural Two-Stage Robust Optimization
Robust optimization provides a mathematical framework for modeling and solving decision-making problems under worst-case uncertainty. This work addresses two-stage robust optimization (2RO) problems (also called adjustable robust optimization), wherein first-stage and second-stage decisions are made before and after uncertainty is realized, respectively. This results in a nested min-max-min optimization problem which is extremely challenging computationally, especially when the decisions are di…

This https://arxiv.org/abs/2304.14907 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

A Stochastic-Gradient-based Interior-Point Algorithm for Solving Smooth Bound-Constrained Optimization Problems
A stochastic-gradient-based interior-point algorithm for minimizing a continuously differentiable objective function (that may be nonconvex) subject to bound constraints is presented, analyzed, and demonstrated through experimental results. The algorithm is unique from other interior-point methods for solving smooth \edit{nonconvex} optimization problems since the search directions are computed using stochastic gradient estimates. It is also unique in its use of inner neighborhoods of the feasi…

The Order Oracle: a New Concept in The Black Box Optimization Problems
Aleksandr Lobanov, Alexander Gasnikov, Andrei Krasnov
https://arxiv.org/abs/2402.09014

The Order Oracle: a New Concept in The Black Box Optimization Problems
Frequently, the burgeoning field of black-box optimization encounters challenges due to a limited understanding of the mechanisms of the objective function. In this paper, we provide the new concept of the "Order Oracle" as a novel approach to solving such problems. The Order Oracle offers a unique perspective, using only access to the order between function values (possibly with some bounded noise), but without assuming access to their values. As theoretical results, we provide estimates of th…

A Proximal Gradient Method with an Explicit Line search for Multiobjective Optimization
Yunier Bello-Cruz, J. G. Melo, L. F. Prudente, R. V. G. Serra
https://arxiv.org/abs/2404.10993

A Proximal Gradient Method with an Explicit Line search for Multiobjective Optimization
We present a proximal gradient method for solving convex multiobjective optimization problems, where each objective function is the sum of two convex functions, with one assumed to be continuously differentiable. The algorithm incorporates a backtracking line search procedure that requires solving only one proximal subproblem per iteration, and is exclusively applied to the differentiable part of the objective functions. Under mild assumptions, we show that the sequence generated by the method …