Tootfinder

"The Art of Solving Impossible Problems" @ Katina Magazine: https://katinamagazine.org/content/article/future-of-work/2025/the-art-of-solving-impossible-problems
"Sometimes the best way to solve a problem is by ad…

RiNNAL : a Riemannian ALM Solver for SDP-RLT Relaxations of Mixed-Binary Quadratic Programs
Di Hou, Tianyun Tang, Kim-Chuan Toh
https://arxiv.org/abs/2507.13776

RiNNAL+: a Riemannian ALM Solver for SDP-RLT Relaxations of Mixed-Binary Quadratic Programs
Doubly nonnegative (DNN) relaxation usually provides a tight lower bound for a mixed-binary quadratic program (MBQP). However, solving DNN problems is challenging because: (1) the problem size is $Ω((n+l)^2)$ for an MBQP with $n$ variables and $l$ inequality constraints, and (2) the rank of optimal solutions cannot be estimated a priori due to the absence of theoretical bounds. In this work, we propose RiNNAL+, a Riemannian augmented Lagrangian method (ALM) for solving DNN problems. We prove t…

Multiphysics embedding localized orthogonal decomposition for thermomechanical coupling problems
Yuzhou Nan, Yajun Wang, Changqing Ye, Xiaofei Guan
https://arxiv.org/abs/2507.13644

Multiphysics embedding localized orthogonal decomposition for thermomechanical coupling problems
Multiscale modeling and analysis of multiphysics coupling processes in highly heterogeneous media present significant challenges. In this paper, we propose a novel multiphysics embedding localized orthogonal decomposition (ME-LOD) method for solving thermomechanical coupling problems, which also provides a systematic approach to address intricate coupling effects in multiphysical systems. Unlike the standard localized orthogonal decomposition (LOD) method that constructs separate multiscale spa…

A Quantum Annealing Approach for Solving Optimal Feature Selection and Next Release Problems
Shuchang Wang, Xiaopeng Qiu, Yingxing Xue, Yanfu Li, Wei Yang
https://arxiv.org/abs/2506.14129

A Quantum Annealing Approach for Solving Optimal Feature Selection and Next Release Problems
Search-based software engineering (SBSE) addresses critical optimization challenges in software engineering, including the next release problem (NRP) and feature selection problem (FSP). While traditional heuristic approaches and integer linear programming (ILP) methods have demonstrated efficacy for small to medium-scale problems, their scalability to large-scale instances remains unknown. Here, we introduce quantum annealing (QA) as a subroutine to tackling multi-objective SBSE problems, leve…

Configurational-force-driven adaptive refinement and coarsening in topology optimization
Gabriel Stankiewicz, Chaitanya Dev, Paul Steinmann
https://arxiv.org/abs/2507.15570

Configurational-force-driven adaptive refinement and coarsening in topology optimization
The iterative nature of topology optimization, especially in combination with nonlinear state problems, often requires the solution of thousands of linear equation systems. Furthermore, due to the pixelated design representation, the use of a fine mesh is essential to obtain geometrically well-defined structures and to accurately compute response quantities such as the von Mises stress. Therefore, the computational cost of solving a fine-mesh topology optimization problem quickly adds up. To ad…

Distortion-Aware Hybrid Beamforming for Integrated Sensing and Communication
Zeyuan Zhang, Yue Xiu, Phee Lep Yeoh, Guangyi Liu, Zixing Wu, Ning Wei
https://arxiv.org/abs/2507.14018

Distortion-Aware Hybrid Beamforming for Integrated Sensing and Communication
This paper investigates a practical partially-connected hybrid beamforming transmitter for integrated sensing and communication (ISAC) with distortion from nonlinear power amplification. For this ISAC system, we formulate a communication rate and sensing mutual information maximization problem driven by our distortion-aware hybrid beamforming design. To address this non-convex problem, we first solve for a fully digital beamforming matrix by alternatively solving three sub-problems using manifo…

Safe and Performant Controller Synthesis using Gradient-based Model Predictive Control and Control Barrier Functions
Aditya Singh, Aastha Mishra, Manan Tayal, Shishir Kolathaya, Pushpak Jagtap
https://arxiv.org/abs/2507.13872

Safe and Performant Controller Synthesis using Gradient-based Model Predictive Control and Control Barrier Functions
Ensuring both performance and safety is critical for autonomous systems operating in real-world environments. While safety filters such as Control Barrier Functions (CBFs) enforce constraints by modifying nominal controllers in real time, they can become overly conservative when the nominal policy lacks safety awareness. Conversely, solving State-Constrained Optimal Control Problems (SC-OCPs) via dynamic programming offers formal guarantees but is intractable in high-dimensional systems. In thi…

Does using machine learning solve our problem of p-hacking and HARKing or do we have the same problems as with statistical tests and models?
https://digiresacademy.kit.com/posts/is-machine-learning-and-ai-solving-the-problem-of-p-hacking

DNA Probe Computing System for Solving NP-Complete Problems
Jin Xu, XiaoLong Shi, Xin Chen, Fang Wang, Sirui Li, Pali Ye, Boliang Zhang, Di Deng, Zheng Kou, Xiaoli Qiang
https://arxiv.org/abs/2507.12470

DNA Probe Computing System for Solving NP-Complete Problems
Efficiently solving NP-complete problems-such as protein structure prediction, cryptographic decryption, and vulnerability detection-remains a central challenge in computer science. Traditional electronic computers, constrained by the Turing machine's one-dimensional data processing and sequential operations, struggle to address these issues effectively. To overcome this bottleneck, computational models must adopt multidimensional data structures and parallel information processing mechanisms. …

Quantum algorithm for solving generalized eigenvalue problems with application to the Schr\"odinger equation
Grzegorz Rajchel-Mieldzio\'c, Szymon Pli\'s, Emil Zak
https://arxiv.org/abs/2506.13534

Quantum algorithm for solving generalized eigenvalue problems with application to the Schrödinger equation
Accurate computation of multiple eigenvalues of quantum Hamiltonians is essential in quantum chemistry, materials science, and molecular spectroscopy. Estimating excited-state energies is challenging for classical algorithms due to exponential scaling with system size, posing an even harder problem than ground-state calculations. We present a quantum algorithm for estimating eigenvalues and singular values of parameterized matrix families, including solving generalized eigenvalue problems that …

Coherent Ising Machines: The Good, The Bad, The Ugly
Farhad Khosravi, Martin Perreault, Artur Scherer, Pooya Ronagh
https://arxiv.org/abs/2507.14489 https:…

Coherent Ising Machines: The Good, The Bad, The Ugly
Analog computing using bosonic computational states is a leading approach to surpassing the computational speed and energy limitations of von Neumann architectures. But the challenges of manufacturing large-scale photonic integrated circuits (PIC) has led to hybrid solutions that integrate optical analog and electronic digital components. A notable example is the coherent Ising machine (CIM), that was primarily invented for solving quadratic binary optimization problems. In this paper, we focus…

A priori error analysis of the proximal Galerkin method
Brendan Keith, Rami Masri, Marius Zeinhofer
https://arxiv.org/abs/2507.13516 https://

A priori error analysis of the proximal Galerkin method
The proximal Galerkin (PG) method is a finite element method for solving variational problems with inequality constraints. It has several advantages, including constraint-preserving approximations and mesh independence. This paper presents the first abstract a priori error analysis of PG methods, providing a general framework to establish convergence and error estimates. As applications of the framework, we demonstrate optimal convergence rates for both the obstacle and Signorini problems using…

On the Effectiveness of Classical Regression Methods for Optimal Switching Problems
Martin Andersson, Benny Avelin, Marcus Olofsson
https://arxiv.org/abs/2506.15436

On the Effectiveness of Classical Regression Methods for Optimal Switching Problems
Simple regression methods provide robust, near-optimal solutions for optimal switching problems in dimensions ranging from 1 to 50. While the theory requires solving intractable PDE systems, the Longstaff-Schwartz algorithm with classical approaches like $k$-NN achieves excellent switching decisions without extensive hyperparameter tuning. Testing eight regression approaches on four benchmark problems, we find that simple methods maintain stable performance across diverse problem characteristic…

Replaced article(s) found for physics.med-ph. https://arxiv.org/list/physics.med-ph/new
[1/1]:
- Solving Blind Inverse Problems: Adaptive Diffusion Models for Motion-corrected Sparse-view 4DCT
Antoine De Paepe, Alexandre Bousse, Cl\'ementine Phung-Ngoc, Dimit…

Double Machine Learning for Conditional Moment Restrictions: IV regression, Proximal Causal Learning and Beyond
Daqian Shao, Ashkan Soleymani, Francesco Quinzan, Marta Kwiatkowska
https://arxiv.org/abs/2506.14950

Double Machine Learning for Conditional Moment Restrictions: IV regression, Proximal Causal Learning and Beyond
Solving conditional moment restrictions (CMRs) is a key problem considered in statistics, causal inference, and econometrics, where the aim is to solve for a function of interest that satisfies some conditional moment equalities. Specifically, many techniques for causal inference, such as instrumental variable (IV) regression and proximal causal learning (PCL), are CMR problems. Most CMR estimators use a two-stage approach, where the first-stage estimation is directly plugged into the second st…

Picat Through the Lens of Advent of Code
Neng-Fa Zhou, Cristian Grozea, H{\aa}kan Kjellerstrand, Ois\'in Mac Fheara\'i
https://arxiv.org/abs/2507.11731

Picat Through the Lens of Advent of Code
Picat is a logic-based, multi-paradigm programming language that integrates features from logic, functional, constraint, and imperative programming paradigms. This paper presents solutions to several problems from the 2024 Advent of Code (AoC). While AoC problems are not designed for any specific programming language, certain problem types, such as reverse engineering and path-finding, are particularly well-suited to Picat due to its built-in constraint solving, pattern matching, backtracking, …

No-dimensional Tverberg-type problems
Alexander Polyanskii
https://arxiv.org/abs/2506.13451 https://arxiv.org/pdf/2506.13451

No-dimensional Tverberg-type problems
Recently, Adiprasito et al. have initiated the study of the so-called no-dimensional Tverberg problem. This problem can be informally stated as follows: Given $n\geq k$, partition an $n$-point set in Euclidean space into $k$ parts such that their convex hulls intersect a ball of relatively small radius. In this survey, we aim to present the recent progress towards solving the no-dimensional Tverberg problem and new open questions arising in its context. Also, we discuss the colorful variation…

Backsolution: A Framework for Solving Inverse Problems via Automatic Differentiation
Koji Kobayashi, Tomi Ohtsuki
https://arxiv.org/abs/2506.13210 https://…

Backsolution: A Framework for Solving Inverse Problems via Automatic Differentiation
We present a simple yet powerful framework for solving inverse problems by leveraging automatic differentiation. Our method is broadly applicable whenever a smooth cost function can be defined near the true solution, and a numerical simulator is available. As a concrete example, we demonstrate that our method can accurately reconstruct the spatial profiles in a conductor from magnetotransport measurements. Even if the given data are insufficient to uniquely determine the profiles, the same fram…

Approaching Optimality for Solving Dense Linear Systems with Low-Rank Structure
Micha{\l} Derezi\'nski, Aaron Sidford
https://arxiv.org/abs/2507.11724 …

Approaching Optimality for Solving Dense Linear Systems with Low-Rank Structure
We provide new high-accuracy randomized algorithms for solving linear systems and regression problems that are well-conditioned except for $k$ large singular values. For solving such $d \times d$ positive definite system our algorithms succeed whp. and run in time $\tilde O(d^2 + k^ω)$. For solving such regression problems in a matrix $\mathbf{A} \in \mathbb{R}^{n \times d}$ our methods succeed whp. and run in time $\tilde O(\mathrm{nnz}(\mathbf{A}) + d^2 + k^ω)$ where $ω$ is the matrix mult…

Adaptive Graph Shrinking for Quantum Optimization of Constrained Combinatorial Problems
Monit Sharma, Hoong Chuin Lau
https://arxiv.org/abs/2506.14250 http…

Adaptive Graph Shrinking for Quantum Optimization of Constrained Combinatorial Problems
A range of quantum algorithms, especially those leveraging variational parameterization and circuit-based optimization, are being studied as alternatives for solving classically intractable combinatorial optimization problems (COPs). However, their applicability is limited by hardware constraints, including shallow circuit depth, limited qubit counts, and noise. To mitigate these issues, we propose a hybrid classical--quantum framework based on graph shrinking to reduce the number of variables …

Uniform stability for the matrix inverse Sturm-Liouville problems
Natalia P. Bondarenko
https://arxiv.org/abs/2506.15300 https://arxi…

Uniform stability for the matrix inverse Sturm-Liouville problems
In this paper, the uniform stability of the inverse spectral problem is proved for the matrix Sturm-Liouville operator on a finite interval. Namely, we describe the sets of spectral data, on which the inverse spectral mapping is bounded and, consequently, the uniform estimates hold for the differences of the matrix potentials and of the corresponding coefficients of the boundary conditions. Our approach is based on a constructive procedure for solving the inverse problem by developing ideas of …

Sequence Modeling for Time-Optimal Quadrotor Trajectory Optimization with Sampling-based Robustness Analysis
Katherine Mao, Hongzhan Yu, Ruipeng Zhang, Igor Spasojevic, M Ani Hsieh, Sicun Gao, Vijay Kumar
https://arxiv.org/abs/2506.13915

Sequence Modeling for Time-Optimal Quadrotor Trajectory Optimization with Sampling-based Robustness Analysis
Time-optimal trajectories drive quadrotors to their dynamic limits, but computing such trajectories involves solving non-convex problems via iterative nonlinear optimization, making them prohibitively costly for real-time applications. In this work, we investigate learning-based models that imitate a model-based time-optimal trajectory planner to accelerate trajectory generation. Given a dataset of collision-free geometric paths, we show that modeling architectures can effectively learn the pat…

Artificial Intelligence for Quantum Matter: Finding a Needle in a Haystack
Khachatur Nazaryan, Filippo Gaggioli, Yi Teng, Liang Fu
https://arxiv.org/abs/2507.13322

Artificial Intelligence for Quantum Matter: Finding a Needle in a Haystack
Neural networks (NNs) have great potential in solving the ground state of various many-body problems. However, several key challenges remain to be overcome before NNs can tackle problems and system sizes inaccessible with more established tools. Here, we present a general and efficient method for learning the NN representation of an arbitrary many-body complex wave function. Having reached overlaps as large as $99.9\%$ for as many as $25$ particles, we employ our neural wave function for pre-tr…

The Pitfalls and Potentials of Adding Gene-invariance to Optimal Mixing
Anton Bouter, Dirk Thierens, Peter A. N. Bosman
https://arxiv.org/abs/2506.15222 ht…

The Pitfalls and Potentials of Adding Gene-invariance to Optimal Mixing
Optimal Mixing (OM) is a variation operator that integrates local search with genetic recombination. EAs with OM are capable of state-of-the-art optimization in discrete spaces, offering significant advantages over classic recombination-based EAs. This success is partly due to high selection pressure that drives rapid convergence. However, this can also negatively impact population diversity, complicating the solving of hierarchical problems, which feature multiple layers of complexity. While t…

Towards Solving More Challenging IMO Problems via Decoupled Reasoning and Proving
Zhenwen Liang, Linfeng Song, Yang Li, Tao Yang, Feng Zhang, Haitao Mi, Dong Yu
https://arxiv.org/abs/2507.06804

Towards Solving More Challenging IMO Problems via Decoupled Reasoning and Proving
Automated Theorem Proving (ATP) in formal languages is a foundational challenge for AI. While Large Language Models (LLMs) have driven remarkable progress, a significant gap remains between their powerful informal reasoning capabilities and their weak formal proving performance. Recent studies show that the informal accuracy exceeds 80% while formal success remains below 8% on benchmarks like PutnamBench. We argue this gap persists because current state-of-the-art provers, by tightly coupling r…

Preemptive Solving of Future Problems: Multitask Preplay in Humans and Machines
Wilka Carvalho, Sam Hall-McMaster, Honglak Lee, Samuel J. Gershman
https://arxiv.org/abs/2507.05561

Preemptive Solving of Future Problems: Multitask Preplay in Humans and Machines
Humans can pursue a near-infinite variety of tasks, but typically can only pursue a small number at the same time. We hypothesize that humans leverage experience on one task to preemptively learn solutions to other tasks that were accessible but not pursued. We formalize this idea as Multitask Preplay, a novel algorithm that replays experience on one task as the starting point for "preplay" -- counterfactual simulation of an accessible but unpursued task. Preplay is used to learn a predictive r…

Imagine if we collectively spent just 10% of the resources that go into the AI bullshit hype machine on solving, you know, the myriad of existential problems humanity faces.

DrafterBench: Benchmarking Large Language Models for Tasks Automation in Civil Engineering
Yinsheng Li, Zhen Dong, Yi Shao
https://arxiv.org/abs/2507.11527

DrafterBench: Benchmarking Large Language Models for Tasks Automation in Civil Engineering
Large Language Model (LLM) agents have shown great potential for solving real-world problems and promise to be a solution for tasks automation in industry. However, more benchmarks are needed to systematically evaluate automation agents from an industrial perspective, for example, in Civil Engineering. Therefore, we propose DrafterBench for the comprehensive evaluation of LLM agents in the context of technical drawing revision, a representation task in civil engineering. DrafterBench contains t…

Watermarking Quantum Neural Networks Based on Sample Grouped and Paired Training
Limengnan Zhou, Hanzhou Wu
https://arxiv.org/abs/2506.12675 https://

Watermarking Quantum Neural Networks Based on Sample Grouped and Paired Training
Quantum neural networks (QNNs) leverage quantum computing to create powerful and efficient artificial intelligence models capable of solving complex problems significantly faster than traditional computers. With the fast development of quantum hardware technology, such as superconducting qubits, trapped ions, and integrated photonics, quantum computers may become reality, accelerating the applications of QNNs. However, preparing quantum circuits and optimizing parameters for QNNs require quantu…

Reasoning Strategies in Large Language Models: Can They Follow, Prefer, and Optimize?
Yanjian Zhang, Guillaume Wisniewski, Nadi Tomeh, Thierry Charnois
https://arxiv.org/abs/2507.11423

Reasoning Strategies in Large Language Models: Can They Follow, Prefer, and Optimize?
Human reasoning involves different strategies, each suited to specific problems. Prior work shows that large language model (LLMs) tend to favor a single reasoning strategy, potentially limiting their effectiveness in diverse reasoning challenges. In this work, we investigate whether prompting can control LLMs reasoning strategies and assess its impact on logical problem-solving. While our experiments show that no single strategy consistently improves accuracy, performance could be enhanced if …

I don't mind solving hard and interesting problems.
But I do get unreasonably angry at tools that so clearly care about only one specific use case and give a big FU to any other, like the one I'm trying to solve.
#Programming #PHP

Solving Distance-Based Optimization Problems Using Optical Hardware
Guangyao Li, Richard Zhipeng Wang, Natalia G. Berloff
https://arxiv.org/abs/2507.11378 …

Solving Distance-Based Optimization Problems Using Optical Hardware
We present a practical approach to solving distance-based optimization problems using optical computing hardware. The objective is to minimize an energy function defined as the weighted sum of squared differences between measured distances and the squared Euclidean distances of point coordinates. By representing coordinates as complex numbers, we map the optimization problem onto optical fields, enabling its solution through either the canonical transformation (CT) method or the gain-based bifu…

Solving Inverse Problems in Stochastic Self-Organising Systems through Invariant Representations
Elias Najarro, Nicolas Bessone, Sebastian Risi
https://arxiv.org/abs/2506.11796

Solving Inverse Problems in Stochastic Self-Organising Systems through Invariant Representations
Self-organising systems demonstrate how simple local rules can generate complex stochastic patterns. Many natural systems rely on such dynamics, making self-organisation central to understanding natural complexity. A fundamental challenge in modelling such systems is solving the inverse problem: finding the unknown causal parameters from macroscopic observations. This task becomes particularly difficult when observations have a strong stochastic component, yielding diverse yet equivalent patter…

Efficient Task Graph Scheduling for Parallel QR Factorization in SLSQP
Soumyajit Chatterjee, Rahul Utkoor, Uppu Eshwar, Sathya Peri, V. Krishna Nandivada
https://arxiv.org/abs/2506.09463

Efficient Task Graph Scheduling for Parallel QR Factorization in SLSQP
Efficient task scheduling is paramount in parallel programming on multi-core architectures, where tasks are fundamental computational units. QR factorization is a critical sub-routine in Sequential Least Squares Quadratic Programming (SLSQP) for solving non-linear programming (NLP) problems. QR factorization decomposes a matrix into an orthogonal matrix Q and an upper triangular matrix R, which are essential for solving systems of linear equations arising from optimization problems. SLSQP uses …

Ensemble of Weak Spectral Total Variation Learners: a PET-CT Case Study
Anna Rosenberg, John Kennedy, Zohar Keidar, Yehoshua Y. Zeevi, Guy Gilboa
https://arxiv.org/abs/2507.08735 …

Ensemble of Weak Spectral Total Variation Learners: a PET-CT Case Study
Solving computer vision problems through machine learning, one often encounters lack of sufficient training data. To mitigate this we propose the use of ensembles of weak learners based on spectral total-variation (STV) features (Gilboa 2014). The features are related to nonlinear eigenfunctions of the total-variation subgradient and can characterize well textures at various scales. It was shown (Burger et-al 2016) that, in the one-dimensional case, orthogonal features are generated, whereas in…

Forward and Inverse Problems for a Langevin-Type Fractional Equation Involving Non-Local Time Condition
Fayziev Yusuf, Jumaeva Shakhnoza
https://arxiv.org/abs/2507.07446

Forward and Inverse Problems for a Langevin-Type Fractional Equation Involving Non-Local Time Condition
The paper addresses the formulation and analysis of direct and inverse problems for a Langevin-type fractional differential equation under a non-local condition imposed on the time variable. An additional condition for solving the inverse problem has the form $u(t_0)=ω$. The existence and uniqueness of a solution to the problems are established, and stability inequalities are derived. Criteria ensuring the uniqueness of the solution are identified.

This https://arxiv.org/abs/2409.08906 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_ees…

Gaussian is All You Need: A Unified Framework for Solving Inverse Problems via Diffusion Posterior Sampling
Diffusion models can generate a variety of high-quality images by modeling complex data distributions. Trained diffusion models can also be very effective image priors for solving inverse problems. Most of the existing diffusion-based methods integrate data consistency steps by approximating the likelihood function within the diffusion reverse sampling process. In this paper, we show that the existing approximations are either insufficient or computationally inefficient. To address these issues…

GPU-Accelerated Simulated Oscillator Ising/Potts Machine Solving Combinatorial Optimization Problems
Yilmaz Ege Gonul, Ceyhun Efe Kayan, Ilknur Mustafazade, Nagarajan Kandasamy, Baris Taskin
https://arxiv.org/abs/2505.22631

GPU-Accelerated Simulated Oscillator Ising/Potts Machine Solving Combinatorial Optimization Problems
Oscillator-based Ising machines (OIMs) and oscillator-based Potts machines (OPMs) have emerged as promising hardware accelerators for solving NP-hard combinatorial optimization problems by leveraging the phase dynamics of coupled oscillators. In this work, a GPU-accelerated simulated OIM/OPM digital computation framework capable of solving combinatorial optimization problems is presented. The proposed implementation harnesses the parallel processing capabilities of GPUs to simulate large-scale …

Lower bound of computational complexity of knapsack problems
Zhidong Zhang
https://arxiv.org/abs/2506.12080 https://arxiv.org/pdf/250…

Lower bound of computational complexity of knapsack problems
The quantum statistics mechanism is very powerful for investigating the equilibrium states and the phase transitions in complex spin disorder systems. The spin disorder systems act as an interdisciplinary platform for solving the optimum processes in computer science. In this work, I determined the lower bound of the computational complexity of knapsack problems. I investigated the origin of nontrivial topological structures in these hard problems. It was uncovered that the nontrivial topologic…

Solving Euclidean Problems by Isotropic Initialization
Khusrav Yorov, Bolun Wang, Mikhail Skopenkov, Helmut Pottmann, Caigui Jiang
https://arxiv.org/abs/2506.01726

Solving Euclidean Problems by Isotropic Initialization
Many problems in Euclidean geometry, arising in computational design and fabrication, amount to a system of constraints, which is challenging to solve. We suggest a new general approach to the solution, which is to start with analogous problems in isotropic geometry. Isotropic geometry can be viewed as a structure-preserving simplification of Euclidean geometry. The solutions found in the isotropic case give insight and can initialize optimization algorithms to solve the original Euclidean prob…

Primer to get you started with Optimization and Mathematical Programming in R #rstats

CRAN Task View: Optimization and Mathematical Programming
This CRAN Task View contains a list of packages that offer facilities for solving optimization problems. Although every regression model in statistics solves an optimization problem, they are not part of this view. If you are looking for regression methods, the following views will also contain useful starting points: MachineLearning, Econometrics, Robust Packages are categorized according to the following sections. See also the “Related Links” and “Other Resources” sections at the end.

Greed is slow on sparse graphs of oriented valued constraints
Artem Kaznatcheev, Sofia Vazquez Alferez
https://arxiv.org/abs/2506.11662 https://

Greed is slow on sparse graphs of oriented valued constraints
Greedy local search is especially popular for solving valued constraint satisfaction problems (VCSPs). Since any method will be slow for some VCSPs, we ask: what is the simplest VCSP on which greedy local search is slow? We construct a VCSP on 6n Boolean variables for which greedy local search takes 7(2^n - 1) steps to find the unique peak. Our VCSP is simple in two ways. First, it is very sparse: its constraint graph has pathwidth 2 and maximum degree 3. This is the simplest VCSP on which some…

Towards solving large QUBO problems using quantum algorithms: improving the LogQ scheme
Yagnik Chatterjee, J\'er\'emie Messud
https://arxiv.org/abs/2507.08489

Towards solving large QUBO problems using quantum algorithms: improving the LogQ scheme
The LogQ algorithm encodes Quadratic Unconstrained Binary Optimization (QUBO) problems with exponentially fewer qubits than the Quantum Approximate Optimization Algorithm (QAOA). The advantages of conventional LogQ are accompanied by a challenge related to the optimization of its free parameters, which requires the usage of resource intensive evolutionary or even global optimization algorithms. We propose a new LogQ parameterization that can be optimized with a gradient-inspired method, which i…

Replaced article(s) found for q-bio.MN. https://arxiv.org/list/q-bio.MN/new
[1/1]:
- Identifying Protein Co-regulatory Network Logic by Solving B-SAT Problems through Gate-based Quan...
Brisebois, Broderick, Khatooni, Wilson, Rayan, Broderick

Monotone and nonmonotone linearized block coordinate descent methods for nonsmooth composite optimization problems
Yassine Nabou, Lahcen El Bourkhissi, Sebastian U. Stich, Tuomo Valkonen
https://arxiv.org/abs/2506.12397

Monotone and nonmonotone linearized block coordinate descent methods for nonsmooth composite optimization problems
In this paper, we introduce both monotone and nonmonotone variants of LiBCoD, a \textbf{Li}nearized \textbf{B}lock \textbf{Co}ordinate \textbf{D}escent method for solving composite optimization problems. At each iteration, a random block is selected, and the smooth components of the objective are linearized along the chosen block in a Gauss-Newton approach. For the monotone variant, we establish a global sublinear convergence rate to a stationary point under the assumption of bounded iterates. …

Evaluating the Effectiveness of Large Language Models in Solving Simple Programming Tasks: A User-Centered Study
Kai Deng
https://arxiv.org/abs/2507.04043 …

Evaluating the Effectiveness of Large Language Models in Solving Simple Programming Tasks: A User-Centered Study
As large language models (LLMs) become more common in educational tools and programming environments, questions arise about how these systems should interact with users. This study investigates how different interaction styles with ChatGPT-4o (passive, proactive, and collaborative) affect user performance on simple programming tasks. I conducted a within-subjects experiment where fifteen high school students participated, completing three problems under three distinct versions of the model. Eac…

Discontinuity-aware KAN-based physics-informed neural networks
Guoqiang Lei, D. Exposito, Xuerui Mao
https://arxiv.org/abs/2507.08338 https://

Discontinuity-aware KAN-based physics-informed neural networks
Physics-informed neural networks (PINNs) have proved to be a promising method for the rapid solving of partial differential equations (PDEs) in both forward and inverse problems. However, due to the smoothness assumption of functions approximated by general neural networks, PINNs are prone to spectral bias and numerical instability and suffer from reduced accuracy when solving PDEs with sharp spatial transitions or fast temporal evolution. To address this limitation, a discontinuity-aware physi…

Non-Asymptotic Analysis of Online Local Private Learning with SGD
Enze Shi, Jinhan Xie, Bei Jiang, Linglong Kong, Xuming He
https://arxiv.org/abs/2507.07041

Non-Asymptotic Analysis of Online Local Private Learning with SGD
Differentially Private Stochastic Gradient Descent (DP-SGD) has been widely used for solving optimization problems with privacy guarantees in machine learning and statistics. Despite this, a systematic non-asymptotic convergence analysis for DP-SGD, particularly in the context of online problems and local differential privacy (LDP) models, remains largely elusive. Existing non-asymptotic analyses have focused on non-private optimization methods, and hence are not applicable to privacy-preservin…

Solving inverse problems of Type IIB flux vacua with conditional generative models
Sven Krippendorf, Zhimei Liu
https://arxiv.org/abs/2506.22551 https://…

Solving inverse problems of Type IIB flux vacua with conditional generative models
We address the inverse problem in Type IIB flux compactifications of identifying flux vacua with targeted phenomenological properties such as specific superpotential values or tadpole constraints using conditional generative models. These machine learning techniques overcome computational bottlenecks in traditional approaches such as rejection sampling and Markov Chain Monte Carlo (MCMC), which struggle to generate rare, finely-tuned vacua. As a proof of concept, we demonstrate that conditional…

Solving Linear Programs with Differential Privacy
Alina Ene, Huy Le Nguyen, Ta Duy Nguyen, Adrian Vladu
https://arxiv.org/abs/2507.10946 https://

Solving Linear Programs with Differential Privacy
We study the problem of solving linear programs of the form $Ax\le b$, $x\ge0$ with differential privacy. For homogeneous LPs $Ax\ge0$, we give an efficient $(ε,δ)$-differentially private algorithm which with probability at least $1-β$ finds in polynomial time a solution that satisfies all but $O(\frac{d^{2}}ε\log^{2}\frac{d}{δβ}\sqrt{\log\frac{1}{ρ_{0}}})$ constraints, for problems with margin $ρ_{0}>0$. This improves the bound of $O(\frac{d^{5}}ε\log^{1.5}\frac{1}{ρ_{0}}\mathrm{poly…

Visual mental imagery and #aphantasia lesions map onto a convergent brain network https://www.medrxiv.org/content/10.1101/2025.05.23.25328072v1 by @…

Visual Mental Imagery and Aphantasia Lesions Map onto a Convergent Brain Network
Background Visual mental imagery, the ability to volitionally form perceptual representations without corresponding external stimuli, allows reliving of past events, solving problems and imagining the future. The absence of visual mental imagery, called aphantasia, has recently been recognized to occur in about 1% of the general population but the cause is uncertain. By studying rare cases of acquired aphantasia we can identify regions that when injured cause loss of visual mental imagery. Met…

Optimal Spectral Approximation in the Overlaps for Generalized Finite Element Methods
Christian Alber, Peter Bastian, Moritz Hauck, Robert Scheichl
https://arxiv.org/abs/2507.12226

Optimal Spectral Approximation in the Overlaps for Generalized Finite Element Methods
In this paper, we study a generalized finite element method for solving second-order elliptic partial differential equations with rough coefficients. The method uses local approximation spaces computed by solving eigenvalue problems on rings around the boundary of local subdomains. Compared to the corresponding method that solves eigenvalue problems on the whole subdomains, the problem size and the bandwidth of the resulting system matrices are substantially reduced, resulting in faster spectra…

Learning to Maximize Quantum Neural Network Expressivity via Effective Rank
Juan Yao
https://arxiv.org/abs/2506.15375 https://arxiv.o…

Learning to Maximize Quantum Neural Network Expressivity via Effective Rank
Quantum neural networks (QNNs) are widely employed as ansätze for solving variational problems, where their expressivity directly impacts performance. Yet, accurately characterizing QNN expressivity remains an open challenge, impeding the optimal design of quantum circuits. In this work, we introduce the effective rank, denoted as $κ$, as a novel quantitative measure of expressivity. Specifically, $κ$ captures the number of effectively independent parameters among all the variational paramet…

Universal Fourier Neural Operators for Micromechanics
Binh Huy Nguyen, Matti Schneider
https://arxiv.org/abs/2507.12233 https://arxiv…

Universal Fourier Neural Operators for Micromechanics
\noindent Solving cell problems in homogenization is hard, and available deep-learning frameworks fail to match the speed and generality of traditional computational frameworks. More to the point, it is generally unclear what to expect of machine-learning approaches, let alone single out which approaches are promising. In the work at hand, we advocate Fourier Neural Operators (FNOs) for micromechanics, empowering them by insights from computational micromechanics methods based on the fast Fouri…

Refactoring Codebases through Library Design
Ziga Kovacic, Celine Lee, Justin Chiu, Wenting Zhao, Kevin Ellis
https://arxiv.org/abs/2506.11058 https://

Refactoring Codebases through Library Design
Maintainable and general software allows developers to build robust applications efficiently, yet achieving these qualities often requires refactoring specialized solutions into reusable components. This challenge becomes particularly relevant as code agents become increasingly accurate at solving isolated programming problems. We investigate code agents' capacity to refactor code in ways supporting growth and reusability. We present both a method and a benchmark for refactoring: Librarian, a s…

A Study on Effective Initial Guess Finding Method Based on B\'ezier Curves: Orbit Determination Applications
Daegyun Choi, Sungwook Yang, Henzeh Leeghim, Donghoon Kim
https://arxiv.org/abs/2506.13921

A Study on Effective Initial Guess Finding Method Based on Bézier Curves: Orbit Determination Applications
In celestial mechanics, proper orbits related to missions are obtained by solving two-point boundary value problems. Since a selection method of initial value affects the convergence of the solution, developing an effective method to find an initial guess is required. In this work, Bézier curves, which can describe complicated curves and surfaces, are utilized to find the initial guess. First, the given problems are transformed into Bézier curves forms, and Bézier curves' control points, whi…

Neural Co-state Regulator: A Data-Driven Paradigm for Real-time Optimal Control with Input Constraints
Lihan Lian, Yuxin Tong, Uduak Inyang-Udoh
https://arxiv.org/abs/2507.12259

Neural Co-state Regulator: A Data-Driven Paradigm for Real-time Optimal Control with Input Constraints
We propose a novel unsupervised learning framework for solving nonlinear optimal control problems (OCPs) with input constraints in real-time. In this framework, a neural network (NN) learns to predict the optimal co-state trajectory that minimizes the control Hamiltonian for a given system, at any system's state, based on the Pontryagin's Minimum Principle (PMP). Specifically, the NN is trained to find the norm-optimal co-state solution that simultaneously satisfies the nonlinear system dynamic…

GPU-Accelerated Distributed QAOA on Large-scale HPC Ecosystems
Zhihao Xu, Srikar Chundury, Seongmin Kim, Amir Shehata, Xinyi Li, Ang Li, Tengfei Luo, Frank Mueller, In-Saeng Suh
https://arxiv.org/abs/2506.10531

GPU-Accelerated Distributed QAOA on Large-scale HPC Ecosystems
Quantum computing holds great potential to accelerate the process of solving complex combinatorial optimization problems. The Distributed Quantum Approximate Optimization Algorithm (DQAOA) addresses high-dimensional, dense problems using current quantum computing techniques and high-performance computing (HPC) systems. In this work, we improve the scalability and efficiency of DQAOA through advanced problem decomposition and parallel execution using message passing on the Frontier CPU/GPU super…

Quantum-inspired algorithm for simulating viral response
D. O. Konina, D. I. Korbashov, I. V. Kovalchuk, A. A. Nizamieva, D. A. Chermoshentsev, A. K. Fedorov
https://arxiv.org/abs/2506.15671

Quantum-inspired algorithm for simulating viral response
Understanding the properties of biological systems is an exciting avenue for applying advanced approaches to solving corresponding computational tasks. A specific class of problems that arises in the resolution of biological challenges is optimization. In this work, we present the results of a proof-of-concept study that applies a quantum-inspired optimization algorithm to simulate a viral response. We formulate an Ising-type model to describe the patterns of gene activity in host responses. Re…

Sampling Theory for Super-Resolution with Implicit Neural Representations
Mahrokh Najaf, Gregory Ongie
https://arxiv.org/abs/2506.09949 https://

Sampling Theory for Super-Resolution with Implicit Neural Representations
Implicit neural representations (INRs) have emerged as a powerful tool for solving inverse problems in computer vision and computational imaging. INRs represent images as continuous domain functions realized by a neural network taking spatial coordinates as inputs. However, unlike traditional pixel representations, little is known about the sample complexity of estimating images using INRs in the context of linear inverse problems. Towards this end, we study the sampling requirements for recove…

Athena: Enhancing Multimodal Reasoning with Data-efficient Process Reward Models
Shuai Wang, Zhenhua Liu, Jiaheng Wei, Xuanwu Yin, Dong Li, Emad Barsoum
https://arxiv.org/abs/2506.09532

Athena: Enhancing Multimodal Reasoning with Data-efficient Process Reward Models
We present Athena-PRM, a multimodal process reward model (PRM) designed to evaluate the reward score for each step in solving complex reasoning problems. Developing high-performance PRMs typically demands significant time and financial investment, primarily due to the necessity for step-level annotations of reasoning steps. Conventional automated labeling methods, such as Monte Carlo estimation, often produce noisy labels and incur substantial computational costs. To efficiently generate high-q…

This https://arxiv.org/abs/2411.15111 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csNE_…

Learnable Activation Functions in Physics-Informed Neural Networks for Solving Partial Differential Equations
We investigate learnable activation functions in Physics-Informed Neural Networks (PINNs) for solving Partial Differential Equations (PDEs), comparing traditional Multilayer Perceptrons (MLPs) with fixed and trainable activations against Kolmogorov-Arnold Networks (KANs) that employ learnable basis functions. While PINNs effectively incorporate physical laws into the learning process, they suffer from convergence and spectral bias problems, which limit their applicability to problems with rapid…

A DC-Reformulation for Gradient-$L^0$-Constrained Problems in Function Spaces
Bastian Dittrich, Evelyn Herberg, Roland Herzog, Georg M\"uller
https://arxiv.org/abs/2506.11917

A DC-Reformulation for Gradient-$L^0$-Constrained Problems in Function Spaces
Cardinality constraints in optimization are commonly of $L^0$-type, and they lead to sparsely supported optimizers. An efficient way of dealing with these constraints algorithmically, when the objective functional is convex, is reformulating the constraint using the difference of suitable $L^1$- and largest-$K$-norms and subsequently solving a sequence of penalized subproblems in the difference-of-convex (DC) class. We extend this DC-reformulation approach to problems with $L^0$-type cardinalit…

Unifying Robot Optimization: Monte Carlo Tree Search with Tensor Factorization
Teng Xue, Amirreza Razmjoo, Yan Zhang, Sylvain Calinon
https://arxiv.org/abs/2507.04949

Unifying Robot Optimization: Monte Carlo Tree Search with Tensor Factorization
Many robotic tasks, such as inverse kinematics, motion planning, and optimal control, can be formulated as optimization problems. Solving these problems involves addressing nonlinear kinematics, complex contact dynamics, and long-horizon planning, each posing distinct challenges for state-of-the-art optimization methods. To efficiently solve a wide range of tasks across varying scenarios, researchers either develop specialized algorithms for the task to achieve, or switch between different fram…

Replaced article(s) found for cs.AI. https://arxiv.org/list/cs.AI/new
[2/5]:
- Solving Probabilistic Verification Problems of Neural Networks using Branch and Bound
David Boetius, Stefan Leue, Tobias Sutter

On Differential Privacy for Adaptively Solving Search Problems via Sketching
Shiyuan Feng, Ying Feng, George Z. Li, Zhao Song, David P. Woodruff, Lichen Zhang
https://arxiv.org/abs/2506.05503

On Differential Privacy for Adaptively Solving Search Problems via Sketching
Recently differential privacy has been used for a number of streaming, data structure, and dynamic graph problems as a means of hiding the internal randomness of the data structure, so that multiple possibly adaptive queries can be made without sacrificing the correctness of the responses. Although these works use differential privacy to show that for some problems it is possible to tolerate $T$ queries using $\widetilde{O}(\sqrt{T})$ copies of a data structure, such results only apply to numer…

A Risk-Aware Adaptive Robust MPC with Learned Uncertainty Quantification
Mingcong Li
https://arxiv.org/abs/2507.11420 https://arxiv.o…

A Risk-Aware Adaptive Robust MPC with Learned Uncertainty Quantification
Solving chance-constrained optimal control problems for systems subject to non-stationary uncertainties is a significant challenge.Conventional robust model predictive control (MPC) often yields excessive conservatism by relying on static worst-case assumptions, while standard stochastic MPC methods struggle when underlying uncertainty distributions are unknown a priori.This article presents a Risk-Aware Adaptive Robust MPC (RAAR-MPC) framework,a hierarchical architecture that systematically or…

Convergence of generalized cross-validation with applications to ill-posed integral equations
Tim Jahn, Mikhail Kirilin
https://arxiv.org/abs/2506.14558 ht…

Convergence of generalized cross-validation with applications to ill-posed integral equations
In this article, we rigorously establish the consistency of generalized cross-validation as a parameter-choice rule for solving inverse problems. We prove that the index chosen by leave-one-out GCV achieves a non-asymptotic, order-optimal error bound with high probability for polynomially ill-posed compact operators. Hereby it is remarkable that the unknown true solution need not satisfy a self-similarity condition, which is generally needed for other heuristic parameter choice rules. We quanti…

This https://arxiv.org/abs/2411.18970 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_ees…

FiRe: Fixed-points of Restoration Priors for Solving Inverse Problems
Selecting an appropriate prior to compensate for information loss due to the measurement operator is a fundamental challenge in imaging inverse problems. Implicit priors based on denoising neural networks have become central to widely-used frameworks such as Plug-and-Play (PnP) algorithms. In this work, we introduce Fixed-points of Restoration (FiRe) priors as a new framework for expanding the notion of priors in PnP to general restoration models beyond traditional denoising models. The key ins…

A reconsideration of quasimonotone variational inequality problems
Meiying Wang, Hongwei Liu, Jun Yang
https://arxiv.org/abs/2506.09389 https://

A reconsideration of quasimonotone variational inequality problems
This paper is based on Tseng's exgradient algorithm for solving variational inequality problems in real Hilbert spaces. Under the assumptions that the cost operator is quasimonotone and Lipschitz continuous, we establish the strong convergence, sublinear convergence, and Q-linear convergence of the algorithm. The results of this paper provide new insights into quasimonotone variational inequality problems, extending and enriching existing results in the literature. Finally, we conduct numerical…

This https://arxiv.org/abs/2503.17797 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csLG_…

Enhancing Fourier Neural Operators with Local Spatial Features
Partial Differential Equation (PDE) problems often exhibit strong local spatial structures, and effectively capturing these structures is critical for approximating their solutions. Recently, the Fourier Neural Operator (FNO) has emerged as an efficient approach for solving these PDE problems. By using parametrization in the frequency domain, FNOs can efficiently capture global patterns. However, this approach inherently overlooks the critical role of local spatial features, as frequency-domain…

Solving engineering eigenvalue problems with neural networks using the Rayleigh quotient
Conor Rowan, John Evans, Kurt Maute, Alireza Doostan
https://arxiv.org/abs/2506.04375

Solving engineering eigenvalue problems with neural networks using the Rayleigh quotient
From characterizing the speed of a thermal system's response to computing natural modes of vibration, eigenvalue analysis is ubiquitous in engineering. In spite of this, eigenvalue problems have received relatively little treatment compared to standard forward and inverse problems in the physics-informed machine learning literature. In particular, neural network discretizations of solutions to eigenvalue problems have seen only a handful of studies. Owing to their nonlinearity, neural network d…

Evaluation of LLMs for mathematical problem solving
Ruonan Wang, Runxi Wang, Yunwen Shen, Chengfeng Wu, Qinglin Zhou, Rohitash Chandra
https://arxiv.org/abs/2506.00309

Evaluation of LLMs for mathematical problem solving
Large Language Models (LLMs) have shown impressive performance on a range of educational tasks, but are still understudied for their potential to solve mathematical problems. In this study, we compare three prominent LLMs, including GPT-4o, DeepSeek-V3, and Gemini-2.0, on three mathematics datasets of varying complexities (GSM8K, MATH500, and UNSW datasets). We take a five-dimensional approach based on the Structured Chain-of-Thought (SCoT) framework to assess final answer correctness, step com…

Cutting Slack: Quantum Optimization with Slack-Free Methods for Combinatorial Benchmarks
Monit Sharma, Hoong Chuin Lau
https://arxiv.org/abs/2507.12159 htt…

Cutting Slack: Quantum Optimization with Slack-Free Methods for Combinatorial Benchmarks
Constraint handling remains a key bottleneck in quantum combinatorial optimization. While slack-variable-based encodings are straightforward, they significantly increase qubit counts and circuit depth, challenging the scalability of quantum solvers. In this work, we investigate a suite of Lagrangian-based optimization techniques including dual ascent, bundle methods, cutting plane approaches, and augmented Lagrangian formulations for solving constrained combinatorial problems on quantum simulat…

Online Block Packing
Ariel Ben Eliezer, Noam Nisan
https://arxiv.org/abs/2507.12357 https://arxiv.org/pdf/2507.12357

Online Block Packing
We consider the algorithmic challenge that is faced by blockchains that have multidimensional block constraints and serve quasi-patient bidders. We provide online approximation algorithms for this problem, thus solving open problems left by [Babaioff and Nisan, EC 2025].

On the robustness of Dirichlet-Neumann coupling schemes for fluid-structure-interaction problems with nearly-closed fluid domains
A. Aissa-Berraies, Ferdinando A. Auricchio, Gertjan van Zwieten, E. Harald van Brummelen
https://arxiv.org/abs/2506.04027

On the robustness of Dirichlet-Neumann coupling schemes for fluid-structure-interaction problems with nearly-closed fluid domains
Partitioned methods for fluid-structure interaction (FSI) involve solving the structural and flow problems sequentially. These methods allow for separate settings for the fluid and solid subsystems and thus modularity, enabling reuse of advanced commercial and open-source software. Most partitioned FSI schemes apply a Dirichlet-Neumann (DN) split of the interface conditions. The DN scheme is adequate in a wide range of applications, but it is sensitive to the added-mass effect, and it is suscep…

Solving Convex-Concave Problems with $\tilde{\mathcal{O}}(\epsilon^{-4/7})$ Second-Order Oracle Complexity
Lesi Chen, Chengchang Liu, Luo Luo, Jingzhao Zhang
https://arxiv.org/abs/2506.08362

Solving Convex-Concave Problems with $\tilde{\mathcal{O}}(ε^{-4/7})$ Second-Order Oracle Complexity
Previous algorithms can solve convex-concave minimax problems $\min_{x \in \mathcal{X}} \max_{y \in \mathcal{Y}} f(x,y)$ with $\mathcal{O}(ε^{-2/3})$ second-order oracle calls using Newton-type methods. This result has been speculated to be optimal because the upper bound is achieved by a natural generalization of the optimal first-order method. In this work, we show an improved upper bound of $\tilde{\mathcal{O}}(ε^{-4/7})$ by generalizing the optimal second-order method for convex optimizat…

Legendre-Gauss-Lobatto Collocation Method for Optimal Control via Polynomial Approximations of Differential Equation Vector Fields
Gabriela Abadia-Doyle, William W. Hager, Anil V. Rao
https://arxiv.org/abs/2506.13938

Legendre-Gauss-Lobatto Collocation Method for Optimal Control via Polynomial Approximations of Differential Equation Vector Fields
A new method is described for solving optimal control problems using direct collocation at Legendre-Gauss-Lobatto points. The approach of this paper employs a polynomial approximation of the right-hand side vector field of the differential equations and leads to the following important outcomes. First, the first-order optimality conditions of the LGL integral form are derived, which lead to a full-rank transformed adjoint system and novel costate estimate. Next, a derivative-like form of the LG…

MultiObjectiveAlgorithms.jl: a Julia package for solving multi-objective optimization problems
Oscar Dowson, Xavier Gandibleux, G\"okhan Kof
https://arxiv.org/abs/2507.05501 …

MultiObjectiveAlgorithms.jl: a Julia package for solving multi-objective optimization problems
We present MultiObjectiveAlgorithms.jl, an open-source Julia library for solving multi-objective optimization problems written in JuMP. MultiObjectiveAlgorithms.jl implements a number of different solution algorithms, which all rely on an iterative scalarization of the problem from a multi-objective optimization problem to a sequence of single-objective subproblems. As part of this work, we extended JuMP to support vector-valued objective functions. Because it is based on JuMP, MultiObjectiveAl…

This https://arxiv.org/abs/2501.02161 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Improved adjoint lattice Boltzmann method for topology optimization of laminar convective heat transfer
Solving flow-related inverse problems such as topology optimization problems is intricate but significant in various engineering fields. The lattice Boltzmann method (LBM) and the related adjoint method are highly suitable to perform sensitivity analysis in flow-related inverse problems thanks to their strong capability to handle complex structures and excellent parallel scalability. However, the current continuous adjoint LBM shows theoretical inconsistency and poor numerical stability for ope…

An Adaptive Order Caputo Fractional Gradient Descent Method for Multi-objective Optimization Problems
Barsha Shaw, Md Abu Talhamainuddin Ansary
https://arxiv.org/abs/2507.07674

An Adaptive Order Caputo Fractional Gradient Descent Method for Multi-objective Optimization Problems
This article introduces the multi-objective adaptive order Caputo fractional gradient descent (MOAOCFGD) algorithm for solving unconstrained multi-objective problems. The proposed method performs equally well for both smooth and non-smooth multi-objective optimization problems. Moreover, the proposed method does not require any a priori chosen parameters or ordering information of the objective functions. At every iteration of the proposed method, a subproblem is solved to identify a suitable d…

Protein folding with an all-to-all trapped-ion quantum computer
Sebasti\'an V. Romero, Alejandro Gomez Cadavid, Pavle Nika\v{c}evi\'c, Enrique Solano, Narendra N. Hegade, Miguel Angel Lopez-Ruiz, Claudio Girotto, Masako Yamada, Panagiotis Kl. Barkoutsos, Ananth Kaushik, Martin Roetteler
https://arxiv.org/abs/2506.07866…

Protein folding with an all-to-all trapped-ion quantum computer
We experimentally demonstrate that the bias-field digitized counterdiabatic quantum optimization (BF-DCQO) algorithm, implemented on IonQ's fully connected trapped-ion quantum processors, offers an efficient approach to solving dense higher-order unconstrained binary optimization (HUBO) problems. Specifically, we tackle protein folding on a tetrahedral lattice for up to 12 amino acids, representing the largest quantum hardware implementations of protein folding problems reported to date. Additi…

Fredholm Neural Networks for forward and inverse problems in elliptic PDEs
Kyriakos Georgiou, Constantinos Siettos, Athanasios N. Yannacopoulos
https://arxiv.org/abs/2507.06038

Fredholm Neural Networks for forward and inverse problems in elliptic PDEs
Building on our previous work introducing Fredholm Neural Networks (Fredholm NNs/ FNNs) for solving integral equations, we extend the framework to tackle forward and inverse problems for linear and semi-linear elliptic partial differential equations. The proposed scheme consists of a deep neural network (DNN) which is designed to represent the iterative process of fixed-point iterations for the solution of elliptic PDEs using the boundary integral method within the framework of potential theory…

An Extended Variational Barzilai-Borwein Method
Xin Xu
https://arxiv.org/abs/2506.12731 https://arxiv.org/pdf/2506.12731

An Extended Variational Barzilai-Borwein Method
The Barzilai-Borwein (BB) method is an effective gradient descent algorithm for solving unconstrained optimization problems. Based on the observation of two classical BB step sizes, by constructing a variational least squares model, we propose a novel class of BB step sizes, each of which still retains the quasi-Newton property, with the original two BB step sizes being their two extreme cases.

Asymmetric Perturbation in Solving Bilinear Saddle-Point Optimization
Kenshi Abe, Mitsuki Sakamoto, Kaito Ariu, Atsushi Iwasaki
https://arxiv.org/abs/2506.05747

Asymmetric Perturbation in Solving Bilinear Saddle-Point Optimization
This paper proposes an asymmetric perturbation technique for solving saddle-point optimization problems, commonly arising in min-max problems, game theory, and constrained optimization. Perturbing payoffs or values are known to be effective in stabilizing learning dynamics and finding an exact solution or equilibrium. However, it requires careful adjustment of the perturbation magnitude; otherwise, learning dynamics converge to only an equilibrium. We establish an impossibility result that it a…

Mixed FEM for coupled unsteady fluid flow problems with $p$-type Brinkman-Forchheimer framework and its application for reverse-osmosis desalination
Zeinab Gharibi, Mostafa Abbaszadeh, Mehdi Dehghan
https://arxiv.org/abs/2507.03974

Mixed FEM for coupled unsteady fluid flow problems with $p$-type Brinkman-Forchheimer framework and its application for reverse-osmosis desalination
This work analyzes a fully discrete mixed finite element method in a Banach space framework for solving nonstationary coupled fluid flow problems modeled by the Brinkman-Forchheimer equations, with applications to reverse osmosis. The model couples unsteady $p$-type convective Brinkman-Forchheimer and transport equations with nonlinear boundary conditions across a semi-permeable membrane. A mixed formulation is used for the fluid equation (pseudostress-velocity) and for the transport equation (…

On the Robustness of Derivative-free Methods for Linear Quadratic Regulator
Weijian Li, Panagiotis Kounatidis, Zhong-Ping Jiang, Andreas A. Malikopoulos
https://arxiv.org/abs/2506.12596

On the Robustness of Derivative-free Methods for Linear Quadratic Regulator
Policy optimization has drawn increasing attention in reinforcement learning, particularly in the context of derivative-free methods for linear quadratic regulator (LQR) problems with unknown dynamics. This paper focuses on characterizing the robustness of derivative-free methods for solving an infinite-horizon LQR problem. To be specific, we estimate policy gradients by cost values, and study the effect of perturbations on the estimations, where the perturbations may arise from function approx…

Warm-starting outer approximation for parametrized convex MINLP
Erik Tamm, Gabriele Eichfelder, Jan Kronqvist
https://arxiv.org/abs/2507.08595 https://

Warm-starting outer approximation for parametrized convex MINLP
We address the challenge of efficiently solving parametrized sequences of convex Mixed-Integer Nonlinear Programming (MINLP) problems through warm-starting techniques. We focus on an outer approximation (OA) approach, for which we develop the theoretical foundation and present two warm-starting techniques for solving sequences of convex MINLPs. These types of problem sequences arise in several important applications, such as, multiobjective MINLPs using scalarization techniques, sparse linear r…

A Quadratic Programming Algorithm with $O(n^3)$ Time Complexity
Liang Wu, Richard D. Braatz
https://arxiv.org/abs/2507.04515 https://…

A Quadratic Programming Algorithm with $O(n^3)$ Time Complexity
Solving linear systems and quadratic programming (QP) problems are both ubiquitous tasks in the engineering and computing fields. Direct methods for solving systems, such as Cholesky, LU, and QR factorizations, exhibit data-independent time complexity of $O(n^3)$. This raises a natural question: could there exist algorithms for solving QPs that also achieve \textit{data-independent} time complexity of $O(n^3)$? This raises a natural question: could there exist algorithms for solving QPs that al…

Was Residual Penalty and Neural Operators All We Needed for Solving Optimal Control Problems?
Oliver G. S. Lundqvist, Fabricio Oliveira
https://arxiv.org/abs/2506.04742

Was Residual Penalty and Neural Operators All We Needed for Solving Optimal Control Problems?
Neural networks have been used to solve optimal control problems, typically by training neural networks using a combined loss function that considers data, differential equation residuals, and objective costs. We show that including cost functions in the training process is unnecessary, advocating for a simpler architecture and streamlined approach by decoupling the optimal control problem from the training process. Thus, our work shows that a simple neural operator architecture, such as DeepON…

Manifolds in Power Systems Optimization
Lucca Rodrigues Pinto, Wilson de Souza Junior, Jaime Laelson Jacob, Luis Alfonso Gallego Pareja, Taufik Abr\~ao
https://arxiv.org/abs/2507.06883

Manifolds in Power Systems Optimization
Manifold optimization (MO) is a powerful mathematical framework that can be applied to solving complex optimization problems with objective functions (OFs) and constraints on complex geometric structures, which is particularly useful in advanced power systems. We explore the application of MO techniques, which offer a robust framework for solving complex, non-convex optimization problems in electrical power distribution systems (EPDS) and electrical power transmission systems (EPTS), particular…

Complexity of normalized stochastic first-order methods with momentum under heavy-tailed noise
Chuan He, Zhaosong Lu, Defeng Sun, Zhanwang Deng
https://arxiv.org/abs/2506.11214

Complexity of normalized stochastic first-order methods with momentum under heavy-tailed noise
In this paper, we propose practical normalized stochastic first-order methods with Polyak momentum, multi-extrapolated momentum, and recursive momentum for solving unconstrained optimization problems. These methods employ dynamically updated algorithmic parameters and do not require explicit knowledge of problem-dependent quantities such as the Lipschitz constant or noise bound. We establish first-order oracle complexity results for finding approximate stochastic stationary points under heavy-t…

On the construction of a gradient method of quadratic optimization, optimal from the point of view of minimizing the distance to the exact solution
N. V. Pletnev
https://arxiv.org/abs/2506.04866

On the construction of a gradient method of quadratic optimization, optimal from the point of view of minimizing the distance to the exact solution
Problems of quadratic optimization in Hilbert space often arise when solving ill-posed problems for differential equations. In this case, the target value of the functional is known. In addition, the structure of the functional allows calculating the gradient by solving well-posed problems, which allows applying first-order methods. This article is devoted to the construction of the $m$-moment minimum error method -- an effective method that minimizes the distance to the exact solution. The con…

Mirror descent for constrained stochastic control problems
Deven Sethi, David \v{S}i\v{s}ka
https://arxiv.org/abs/2506.02564 https://…

Mirror descent for constrained stochastic control problems
Mirror descent is a well established tool for solving convex optimization problems with convex constraints. This article introduces continuous-time mirror descent dynamics for approximating optimal Markov controls for stochastic control problems with the action space being bounded and convex. We show that if the Hamiltonian is uniformly convex in its action variable then mirror descent converges linearly while if it is uniformly strongly convex relative to an appropriate Bregman divergence, the…

Regularized Extragradient Methods for Solving Equilibrium Problems on Hadamard Manifolds
Shikher Sharmaa, Pankaj Gautam, Simeon Reich
https://arxiv.org/abs/2506.22391

Regularized Extragradient Methods for Solving Equilibrium Problems on Hadamard Manifolds
Employing two distinct types of regularization terms, we propose two regularized extragradient methods for solving equilibrium problems on Hadamard manifolds. The sequences generated by these extragradient algorithms converge to a solution of the equilibrium problem without requiring the Lipschitz continuity of the bifunction or imposing additional conditions on the parameters. We establish convergence results for both algorithms and derive global error bounds along with $R$-linear convergence …

A derivative-free regularization algorithm for equality constrained nonlinear least squares problems
Xi Chen, Jinyan Fan
https://arxiv.org/abs/2507.05623 h…

A derivative-free regularization algorithm for equality constrained nonlinear least squares problems
In this paper, we study the equality constrained nonlinear least squares problem, where the Jacobian matrices of the objective function and constraints are unavailable or expensive to compute. We approximate the Jacobian matrices via orthogonal spherical smoothing and propose a derivative-free regularization algorithm for solving the problem. At each iteration, a regularized augmented Lagrangian subproblem is solved to obtain a Newton-like step. If a sufficient decrease in the merit function of…

Augmented Lagrangian methods for infeasible convex optimization problems and diverging proximal-point algorithms
Roland Andrews, Justin Carpentier, Adrien Taylor
https://arxiv.org/abs/2506.22428

Augmented Lagrangian methods for infeasible convex optimization problems and diverging proximal-point algorithms
This work investigates the convergence behavior of augmented Lagrangian methods (ALMs) when applied to convex optimization problems that may be infeasible. ALMs are a popular class of algorithms for solving constrained optimization problems. We establish progressively stronger convergence results, ranging from basic sequence convergence to precise convergence rates, under a hierarchy of assumptions. In particular, we demonstrate that, under mild assumptions, the sequences of iterates generated …

Bregman proximal gradient method for linear optimization under entropic constraints
Luis M. Brice\~no-Arias, Ma\"el Le Treust
https://arxiv.org/abs/2506.10849

Bregman proximal gradient method for linear optimization under entropic constraints
In this paper, we present an efficient algorithm for solving a linear optimization problem with entropic constraints -- a class of problems that arises in game theory and information theory. Our analysis distinguishes between the cases of active and inactive constraints, addressing each using a Bregman proximal gradient method with entropic Legendre functions, for which we establish an ergodic convergence rate of $O(1/n)$ in objective values. For a specific cost structure, our framework provide…

A Computationally Efficient Method for Solving Mixed-Integer AC Optimal Power Flow Problems
Johannes Heid, Nils Bornhorst, Eric T\"onges, Philipp H\"artel, Denis Mende, Martin Braun
https://arxiv.org/abs/2506.18301

A Computationally Efficient Method for Solving Mixed-Integer AC Optimal Power Flow Problems
Stepwise controllable devices, such as switched capacitors or stepwise controllable loads and generators, transform the nonconvex AC optimal power flow (AC-OPF) problem into a nonconvex mixed-integer (MI) programming problem which is generally hard to solve optimally. Existing methods for solving MI-AC-OPF problems usually suffer from either limited accuracy or computational intractability, making them impractical for real-world applications. To address these challenges, we propose an efficient…

Regularization of Nonlinear Inverse Problems -- From Functional Analysis to Data-Driven Approaches
Clemens Kirisits, Bochra Mejri, Sergei Pereverzev, Otmar Scherzer, Cong Shi
https://arxiv.org/abs/2506.17465

Regularization of Nonlinear Inverse Problems -- From Functional Analysis to Data-Driven Approaches
The focus of this book is on the analysis of regularization methods for solving \emph{nonlinear inverse problems}. Specifically, we place a strong emphasis on techniques that incorporate supervised or unsupervised data derived from prior experiments. This approach enables the integration of data-driven insights into the solution of inverse problems governed by physical models. \emph{Inverse problems}, in general, aim to uncover the \emph{inner mechanisms} of an observed system based on indirect…