Tootfinder

This https://arxiv.org/abs/2302.11887 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csLO_…

A Curry-Howard Correspondence for Linear, Reversible Computation
In this paper, we present a linear and reversible programming language with inductives types and recursion. The semantics of the languages is based on pattern-matching; we show how ensuring syntactical exhaustivity and non-overlapping of clauses is enough to ensure reversibility. The language allows to represent any Primitive Recursive Function. We then give a Curry-Howard correspondence with the logic $μ$MALL: linear logic extended with least fixed points allowing inductive statements. The cr…

Optimal Planning for Timed Partial Order Specifications
Kandai Watanabe, Georgios Fainekos, Bardh Hoxha, Morteza Lahijanian, Hideki Okamoto, Sriram Sankaranarayanan
https://arxiv.org/abs/2405.00687

Optimal Planning for Timed Partial Order Specifications
This paper addresses the challenge of planning a sequence of tasks to be performed by multiple robots while minimizing the overall completion time subject to timing and precedence constraints. Our approach uses the Timed Partial Orders (TPO) model to specify these constraints. We translate this problem into a Traveling Salesman Problem (TSP) variant with timing and precedent constraints, and we solve it as a Mixed Integer Linear Programming (MILP) problem. Our contributions include a general pl…

Joint Chance Constrained Optimal Control via Linear Programming
Niklas Schmid, Marta Fochesato, Tobias Sutter, John Lygeros
https://arxiv.org/abs/2402.19360

Joint Chance Constrained Optimal Control via Linear Programming
We establish a linear programming formulation for the solution of joint chance constrained optimal control problems over finite time horizons. The joint chance constraint may represent an invariance, reachability or reach-avoid specification that the trajectory must satisfy with a predefined probability. Compared to the existing literature, the formulation is computationally tractable and the solution exact.

Improving the accuracy and consistency of the energy quadratization method with an energy-optimized technique
Xiaoqing Meng, Aijie Cheng, Zhengguang Liu
https://arxiv.org/abs/2404.01747

Improving the accuracy and consistency of the energy quadratization method with an energy-optimized technique
We propose an energy-optimized invariant energy quadratization method to solve the gradient flow models in this paper, which requires only one linear energy-optimized step to correct the auxiliary variables on each time step. In addition to inheriting the benefits of the baseline and relaxed invariant energy quadratization method, our approach has several other advantages. Firstly, in the process of correcting auxiliary variables, we can directly solve linear programming problem by the energy-o…

Linear Programming in Isabelle/HOL
Julian Parsert
https://arxiv.org/abs/2403.19639 https://arxiv.org/pdf/2403.19639

Linear Programming in Isabelle/HOL
Linear programming describes the problem of optimising a linear objective function over a set of constraints on its variables. In this paper we present a solver for linear programs implemented in the proof assistant Isabelle/HOL. This allows formally proving its soundness, termination, and other properties. We base these results on a previous formalisation of the simplex algorithm which does not take optimisation problems into account. Using the weak duality theorem of linear programming we obt…

Computer classification of linear codes based on lattice point enumeration and integer linear programming
Sascha Kurz
https://arxiv.org/abs/2403.17509 http…

Computer classification of linear codes based on lattice point enumeration and integer linear programming
Linear codes play a central role in coding theory and have applications in several branches of mathematics. For error correction purposes the minimum Hamming distance should be as large as possible. Linear codes related to applications in Galois Geometry often require a certain divisibility of the occurring weights. In this paper we present an algorithmic framework for the classification of linear codes over finite fields with restricted sets of weights. The underlying algorithms are based on l…

Linear Programming in Isabelle/HOL
Julian Parsert
https://arxiv.org/abs/2403.19639 https://arxiv.org/pdf/2403.19639

Linear Programming in Isabelle/HOL
Linear programming describes the problem of optimising a linear objective function over a set of constraints on its variables. In this paper we present a solver for linear programs implemented in the proof assistant Isabelle/HOL. This allows formally proving its soundness, termination, and other properties. We base these results on a previous formalisation of the simplex algorithm which does not take optimisation problems into account. Using the weak duality theorem of linear programming we obt…

A Primal-Dual Frank-Wolfe Algorithm for Linear Programming
Matthew Hough, Stephen A. Vavasis
https://arxiv.org/abs/2402.18514 https://

A Primal-Dual Frank-Wolfe Algorithm for Linear Programming
We present two first-order primal-dual algorithms for solving saddle point formulations of linear programs, namely FWLP (Frank-Wolfe Linear Programming) and FWLP-P. The former iteratively applies the Frank-Wolfe algorithm to both the primal and dual of the saddle point formulation of a standard-form LP. The latter is a modification of FWLP in which regularizing perturbations are used in computing the iterates. We show that FWLP-P converges to a primal-dual solution with error $O(1/\sqrt{k})$ af…

NeuroLGP-SM: A Surrogate-assisted Neuroevolution Approach using Linear Genetic Programming
Fergal Stapleton, Brendan Cody-Kenny, Edgar Galv\'an
https://arxiv.org/abs/2403.19459

NeuroLGP-SM: A Surrogate-assisted Neuroevolution Approach using Linear Genetic Programming
Evolutionary algorithms are increasingly recognised as a viable computational approach for the automated optimisation of deep neural networks (DNNs) within artificial intelligence. This method extends to the training of DNNs, an approach known as neuroevolution. However, neuroevolution is an inherently resource-intensive process, with certain studies reporting the consumption of thousands of GPU days for refining and training a single DNN network. To address the computational challenges associa…

Designing Robust Linear Output Feedback Controller based on CLF-CBF framework via Linear~Programming(LP-CLF-CBF)
Mahroo Bahreinian, Mehdi Kermanshah, Roberto Tron
https://arxiv.org/abs/2403.14519

Designing Robust Linear Output Feedback Controller based on CLF-CBF framework via Linear~Programming(LP-CLF-CBF)
We consider the problem of designing output feedback controllers that use measurements from a set of landmarks to navigate through a cell-decomposable environment using duality, Control Lyapunov and Barrier Functions (CLF, CBF), and Linear Programming. We propose two objectives for navigating in an environment, one to traverse the environment by making loops and one by converging to a stabilization point while smoothing the transition between consecutive cells. We test our algorithms in a simul…

KnapsackLB: Enabling Performance-Aware Layer-4 Load Balancing
Rohan Gandhi, Srinivas Narayana
https://arxiv.org/abs/2404.17783 https://

KnapsackLB: Enabling Performance-Aware Layer-4 Load Balancing
Layer-4 load balancer (LB) is a key building block of online services. In this paper, we empower such LBs to adapt to different and dynamic performance of backend instances (DIPs). Our system, KNAPSACKLB, is generic (can work with variety of LBs), does not require agents on DIPs, LBs or clients, and scales to large numbers of DIPs. KNAPSACKLB uses judicious active probes to learn a mapping from LB weights to the response latency of each DIP, and then applies Integer Linear Programming (ILP) to …

Besicovitch's 1/2 problem and linear programming
Camillo De Lellis, Federico Glaudo, Annalisa Massaccesi, Davide Vittone
https://arxiv.org/abs/2404.17536

Besicovitch's 1/2 problem and linear programming
We consider the following classical conjecture of Besicovitch: a $1$-dimensional Borel set in the plane with finite Hausdorff $1$-dimensional measure $\mathcal{H}^1$ which has lower density strictly larger than $\frac{1}{2}$ almost everywhere must be countably rectifiable. We improve the best known bound, due to Preiss and Tišer, showing that the statement is indeed true if $\frac{1}{2}$ is replaced by $\frac{7}{10}$ (in fact we improve the Preiss-Tišer bound even for the corresponding statem…

skscope: Fast Sparsity-Constrained Optimization in Python
Zezhi Wang, Jin Zhu, Peng Chen, Huiyang Peng, Xiaoke Zhang, Anran Wang, Yu Zheng, Junxian Zhu, Xueqin Wang
https://arxiv.org/abs/2403.18540

skscope: Fast Sparsity-Constrained Optimization in Python
Applying iterative solvers on sparsity-constrained optimization (SCO) requires tedious mathematical deduction and careful programming/debugging that hinders these solvers' broad impact. In the paper, the library skscope is introduced to overcome such an obstacle. With skscope, users can solve the SCO by just programming the objective function. The convenience of skscope is demonstrated through two examples in the paper, where sparse linear regression and trend filtering are addressed with just …

Improving the Bit Complexity of Communication for Distributed Convex Optimization
Mehrdad Ghadiri, Yin Tat Lee, Swati Padmanabhan, William Swartworth, David Woodruff, Guanghao Ye
https://arxiv.org/abs/2403.19146

Improving the Bit Complexity of Communication for Distributed Convex Optimization
We consider the communication complexity of some fundamental convex optimization problems in the point-to-point (coordinator) and blackboard communication models. We strengthen known bounds for approximately solving linear regression, $p$-norm regression (for $1\leq p\leq 2$), linear programming, minimizing the sum of finitely many convex nonsmooth functions with varying supports, and low rank approximation; for a number of these fundamental problems our bounds are nearly optimal, as proven by …

Learning to Cut via Hierarchical Sequence/Set Model for Efficient Mixed-Integer Programming
Jie Wang, Zhihai Wang, Xijun Li, Yufei Kuang, Zhihao Shi, Fangzhou Zhu, Mingxuan Yuan, Jia Zeng, Yongdong Zhang, Feng Wu
https://arxiv.org/abs/2404.12638

Learning to Cut via Hierarchical Sequence/Set Model for Efficient Mixed-Integer Programming
Cutting planes (cuts) play an important role in solving mixed-integer linear programs (MILPs), which formulate many important real-world applications. Cut selection heavily depends on (P1) which cuts to prefer and (P2) how many cuts to select. Although modern MILP solvers tackle (P1)-(P2) by human-designed heuristics, machine learning carries the potential to learn more effective heuristics. However, many existing learning-based methods learn which cuts to prefer, neglecting the importance of l…

This https://arxiv.org/abs/2303.15600 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Finite Representation of Quantile Sets for Multivariate Data via Vector Linear Programming
Empirical quantiles for finitely distributed univariate random variables can be obtained by solving a certain linear program. It is shown in this short note that multivariate empirical quantiles can be obtained in a very similar way by solving a vector linear program. This connection provides a new approach for computing Tukey depth regions and more general cone quantile sets.

This https://arxiv.org/abs/2105.08419 has been replaced.
link: https://scholar.google.com/scholar?q=a

A sparse ADMM-based solver for linear MPC subject to terminal quadratic constraint
Model Predictive Control (MPC) typically includes a terminal constraint to guarantee stability of the closed-loop system under nominal conditions. In linear MPC this constraint is generally taken on a polyhedral set, leading to a quadratic optimization problem. However, the use of an ellipsoidal terminal constraint may be desirable, leading to an optimization problem with a quadratic constraint. In this case, the optimization problem can be solved using Second Order Cone (SOC) programming solve…

This https://arxiv.org/abs/2403.08435 has been replaced.
link: https://scholar.google.com/scholar?q=a

Asymptotic behaviour of integer programming and the $\text{v}$-function of a graded filtration
The $\text{v}$-function of a graded filtration $\mathcal{I}=\{I_{[k]}\}_{k\ge0}$ is introduced. Under the assumption that $\mathcal{I}$ is Noetherian, we prove that the $\text{v}$-function $\text{v}(I_{[k]})$ is an eventually quasi-linear function. This result applies to several situations, including ordinary powers, and integral closures of ordinary powers, among others. As another application, we investigate the asymptotic behaviour of certain integer programming problems. Finally, we present…

This https://arxiv.org/abs/2311.03215 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_qu…

Quantum speedups for linear programming via interior point methods
We describe a quantum algorithm based on an interior point method for solving a linear program with $n$ inequality constraints on $d$ variables. The algorithm explicitly returns a feasible solution that is $\varepsilon$-close to optimal, and runs in time $\sqrt{n} \cdot \mathrm{poly}(d,\log(n),\log(1/\varepsilon))$ which is sublinear for tall linear programs (i.e., $n \gg d$). Our algorithm speeds up the Newton step in the state-of-the-art interior point method of Lee and Sidford [FOCS~'14]. Th…

Constraint Propagation on GPU: A Case Study for the Bin Packing Constraint
Fabio Tardivo, Laurent Michel, Enrico Pontelli
https://arxiv.org/abs/2402.14821 …

Constraint Propagation on GPU: A Case Study for the Bin Packing Constraint
The Bin Packing Problem is one of the most important problems in discrete optimization, as it captures the requirements of many real-world problems. Because of its importance, it has been approached with the main theoretical and practical tools. Resolution approaches based on Linear Programming are the most effective, while Constraint Programming proves valuable when the Bin Packing Problem is a component of a larger problem. This work focuses on the Bin Packing constraint and explores how GPUs…

LLAMP: Assessing Network Latency Tolerance of HPC Applications with Linear Programming
Siyuan Shen, Langwen Huang, Marcin Chrapek, Timo Schneider, Jai Dayal, Manisha Gajbe, Robert Wisniewski, Torsten Hoefler
https://arxiv.org/abs/2404.14193

LLAMP: Assessing Network Latency Tolerance of HPC Applications with Linear Programming
The shift towards high-bandwidth networks driven by AI workloads in data centers and HPC clusters has unintentionally aggravated network latency, adversely affecting the performance of communication-intensive HPC applications. As large-scale MPI applications often exhibit significant differences in their network latency tolerance, it is crucial to accurately determine the extent of network latency an application can withstand without significant performance degradation. Current approaches to as…

Energy bounds for weighted spherical codes and designs via linear programming
Sergiy Borodachov, Peter Boyvalenkov, Peter Dragnev, Douglas Hardin, Edward Saff, Maya Stoyanova
https://arxiv.org/abs/2403.07457

Energy bounds for weighted spherical codes and designs via linear programming
Universal bounds for the potential energy of weighted spherical codes are obtained by linear programming. The universality is in the sense of Cohn-Kumar -- every attaining code is optimal with respect to a large class of potential functions (absolutely monotone), in the sense of Levenshtein -- there is a bound for every weighted code, and in the sense of parameters (nodes and weights) -- they are independent of the potential function. We derive a necessary condition for optimality (in the linea…

Integer Programming for Learning Directed Acyclic Graphs from Non-identifiable Gaussian Models
Tong Xu, Armeen Taeb, Simge K\"u\c{c}\"ukyavuz, Ali Shojaie
https://arxiv.org/abs/2404.12592

Integer Programming for Learning Directed Acyclic Graphs from Non-identifiable Gaussian Models
We study the problem of learning directed acyclic graphs from continuous observational data, generated according to a linear Gaussian structural equation model. State-of-the-art structure learning methods for this setting have at least one of the following shortcomings: i) they cannot provide optimality guarantees and can suffer from learning sub-optimal models; ii) they rely on the stringent assumption that the noise is homoscedastic, and hence the underlying model is fully identifiable. We ov…

Cell-Constrained Particles for Incompressible Fluids
Zohar Levi
https://arxiv.org/abs/2402.17088 https://arxiv.org/pdf/2402.17088

Cell-Constrained Particles for Incompressible Fluids
Incompressibility is a fundamental condition in most fluid models. Accumulation of simulation errors violates it and causes volume loss. Past work suggested correction methods to battle it. These methods, however, are imperfect and in some cases inadequate. We present a method for fluid simulation that strictly enforces incompressibility based on a grid-related definition of discrete incompressibility. We formulate a linear programming (LP) problem that bounds the number of particles that end…

This https://arxiv.org/abs/2311.01959 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

A First Order Method for Linear Programming Parameterized by Circuit Imbalance
Various first order approaches have been proposed in the literature to solve Linear Programming (LP) problems, recently leading to practically efficient solvers for large-scale LPs. From a theoretical perspective, linear convergence rates have been established for first order LP algorithms, despite the fact that the underlying formulations are not strongly convex. However, the convergence rate typically depends on the Hoffman constant of a large matrix that contains the constraint matrix, as we…

The Power of Linear Programming in Sponsored Listings Ranking: Evidence from Field Experiments
Haihao Lu, Luyang Zhang
https://arxiv.org/abs/2403.14862 htt…

The Power of Linear Programming in Sponsored Listings Ranking: Evidence from Field Experiments
Sponsored listing is one of the major revenue sources for many prominent online marketplaces, such as Amazon, Walmart, and Alibaba. When consumers visit a marketplace's webpage for a specific item, in addition to that item, the marketplace might also display a ranked listing of sponsored items from various third-party sellers. These sellers are charged an advertisement fee if a user purchases any of the sponsored items from this listing. Determining how to rank these sponsored items for each in…

Towards Efficient Pareto-optimal Utility-Fairness between Groups in Repeated Rankings
Phuong Dinh Mai, Duc-Trong Le, Tuan-Anh Hoang, Dung D. Le
https://arxiv.org/abs/2402.14305

Towards Efficient Pareto-optimal Utility-Fairness between Groups in Repeated Rankings
In this paper, we tackle the problem of computing a sequence of rankings with the guarantee of the Pareto-optimal balance between (1) maximizing the utility of the consumers and (2) minimizing unfairness between producers of the items. Such a multi-objective optimization problem is typically solved using a combination of a scalarization method and linear programming on bi-stochastic matrices, representing the distribution of possible rankings of items. However, the above-mentioned approach reli…

This https://arxiv.org/abs/2303.15600 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Finite Representation of Quantile Sets for Multivariate Data via Vector Linear Programming
Empirical quantiles for finitely distributed univariate random variables can be obtained by solving a certain linear program. It is shown in this short note that multivariate empirical quantiles can be obtained in a very similar way by solving a vector linear program. This connection provides a new approach for computing Tukey depth regions and more general cone quantile sets.

State-Augmented Linear Games with Antagonistic Error for High-Dimensional, Nonlinear Hamilton-Jacobi Reachability
Will Sharpless, Yat Tin Chow, Sylvia Herbert
https://arxiv.org/abs/2403.16982

State-Augmented Linear Games with Antagonistic Error for High-Dimensional, Nonlinear Hamilton-Jacobi Reachability
Hamilton-Jacobi Reachability (HJR) is a popular method for analyzing the liveness and safety of a dynamical system with bounded control and disturbance. The corresponding HJ value function offers a robust controller and characterizes the reachable sets, but is traditionally solved with Dynamic Programming (DP) and limited to systems of dimension less than six. Recently, the space-parallelizeable, generalized Hopf formula has been shown to also solve the HJ value with a nearly three-log increase…

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…

This https://arxiv.org/abs/2402.16814 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csDM_…

Cut Facets and Cube Facets of Lifted Multicut Polytopes
The lifted multicut problem has diverse applications in the field of computer vision. Exact algorithms based on linear programming require an understanding of lifted multicut polytopes. Despite recent progress, two fundamental questions about these polytopes have remained open: Which lower cube inequalities define facets, and which cut inequalities define facets? In this article, we answer the first question by establishing conditions that are necessary, sufficient and efficiently decidable. To…

This https://arxiv.org/abs/2311.03215 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_qu…

Quantum speedups for linear programming via interior point methods
We describe a quantum algorithm based on an interior point method for solving a linear program with $n$ inequality constraints on $d$ variables. The algorithm explicitly returns a feasible solution that is $\varepsilon$-close to optimal, and runs in time $\sqrt{n} \cdot \mathrm{poly}(d,\log(n),\log(1/\varepsilon))$ which is sublinear for tall linear programs (i.e., $n \gg d$). Our algorithm speeds up the Newton step in the state-of-the-art interior point method of Lee and Sidford [FOCS~'14]. Th…

This https://arxiv.org/abs/2401.11567 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Deterministic Multi-stage Constellation Reconfiguration Using Integer Linear Programming and Sequential Decision-Making Methods
In this paper, we address the problem of reconfiguring Earth observation satellite constellation systems through multiple stages. The Multi-stage Constellation Reconfiguration Problem (MCRP) aims to maximize the total observation rewards obtained by covering a set of targets of interest through the active manipulation of the orbits and relative phasing of constituent satellites. In this paper, we consider deterministic problem settings in which the targets of interest are known a priori. We pro…

Integer Programming for Learning Directed Acyclic Graphs from Non-identifiable Gaussian Models
Tong Xu, Armeen Taeb, Simge K\"u\c{c}\"ukyavuz, Ali Shojaie
https://arxiv.org/abs/2404.12592

Integer Programming for Learning Directed Acyclic Graphs from Non-identifiable Gaussian Models
We study the problem of learning directed acyclic graphs from continuous observational data, generated according to a linear Gaussian structural equation model. State-of-the-art structure learning methods for this setting have at least one of the following shortcomings: i) they cannot provide optimality guarantees and can suffer from learning sub-optimal models; ii) they rely on the stringent assumption that the noise is homoscedastic, and hence the underlying model is fully identifiable. We ov…

This https://arxiv.org/abs/2209.01146 has been replaced.
link: https://scholar.google.com/scholar?q=a

Generalized Principal-Agency: Contracts, Information, Games and Beyond
In the principal-agent problem formulated by Myerson'82, agents have private information (type) and make private decisions (action), both of which are unobservable to the principal. Myerson pointed out an elegant linear programming solution that relies on the revelation principle. This paper extends Myerson's results to a more general setting where the principal's action space can be infinite and subject to additional design constraints. Our generalized principal-agent model unifies several i…

This https://arxiv.org/abs/2401.03252 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

New Lower Bounds for the Schur-Siegel-Smyth Trace Problem
We derive and implement a new way to find lower bounds on the smallest limiting trace-to-degree ratio of totally positive algebraic integers and improve the previously best-known bound to 1.798249. Our method adds new constraints to Smyth's linear programming method to decrease the variables required in the new problem of interest. This allows for faster convergence recovering Schur's bound in the simplest case and Siegel's bound in the second simplest case of our new family of bounds. We als…

This https://arxiv.org/abs/2404.10261 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_sta…

Lighter, Better, Faster Multi-Source Domain Adaptation with Gaussian Mixture Models and Optimal Transport
In this paper, we tackle Multi-Source Domain Adaptation (MSDA), a task in transfer learning where one adapts multiple heterogeneous, labeled source probability measures towards a different, unlabeled target measure. We propose a novel framework for MSDA, based on Optimal Transport (OT) and Gaussian Mixture Models (GMMs). Our framework has two key advantages. First, OT between GMMs can be solved efficiently via linear programming. Second, it provides a convenient model for supervised learning, e…

This https://arxiv.org/abs/2311.15865 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_…

A precise symbolic emulator of the linear matter power spectrum
Computing the matter power spectrum, $P(k)$, as a function of cosmological parameters can be prohibitively slow in cosmological analyses, hence emulating this calculation is desirable. Previous analytic approximations are insufficiently accurate for modern applications, so black-box, uninterpretable emulators are often used. We utilise an efficient genetic programming based symbolic regression framework to explore the space of potential mathematical expressions which can approximate the power s…

This https://arxiv.org/abs/2302.03977 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

On the Circuit Diameter Conjecture for Counterexamples to the Hirsch Conjecture
Circuit diameters of polyhedra are a fundamental tool for studying the complexity of circuit augmentation schemes for linear programming and for finding lower bounds on combinatorial diameters. The main open problem in this area is the circuit diameter conjecture, the analogue of the Hirsch conjecture in the circuit setting. A natural question is whether the well-known counterexamples to the Hirsch conjecture carry over. Previously, Stephen and Yusun showed that the Klee-Walkup counterexample t…

This https://arxiv.org/abs/2403.08435 has been replaced.
link: https://scholar.google.com/scholar?q=a

Asymptotic behaviour of integer programming and the $\text{v}$-function of a graded filtration
The $\text{v}$-function of a graded filtration $\mathcal{I}=\{I_{[k]}\}_{k\ge0}$ is introduced. Under the assumption that $\mathcal{I}$ is Noetherian, we prove that the $\text{v}$-function $\text{v}(I_{[k]})$ is an eventually quasi-linear function. This result applies to several situations, including ordinary powers, and integral closures of ordinary powers, among others. As another application, we investigate the asymptotic behaviour of certain integer programming problems. Finally, we present…

This https://arxiv.org/abs/2311.05595 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

An efficient topology optimization algorithm for large-scale three-dimensional structures
Designing the topology of three-dimensional structures is a challenging problem due to its memory and time consumption. In this paper, we present a robust and efficient algorithm for solving large-scale 3D topology optimization problems. The robustness of the algorithm is ensured by adopting a globally convergent sequential linear programming method with a stopping criterion based on the first-order optimality conditions of the nonlinear problem. To increase the algorithm's efficiency, it is co…

Analytical Heterogeneous Die-to-Die 3D Placement with Macros
Yuxuan Zhao, Peiyu Liao, Siting Liu, Jiaxi Jiang, Yibo Lin, Bei Yu
https://arxiv.org/abs/2403.09070

Analytical Heterogeneous Die-to-Die 3D Placement with Macros
This paper presents an innovative approach to 3D mixed-size placement in heterogeneous face-to-face (F2F) bonded 3D ICs. We propose an analytical framework that utilizes a dedicated density model and a bistratal wirelength model, effectively handling macros and standard cells in a 3D solution space. A novel 3D preconditioner is developed to resolve the topological and physical gap between macros and standard cells. Additionally, we propose a mixed-integer linear programming (MILP) formulation f…

Conservative Linear Envelopes for High-Dimensional, Hamilton-Jacobi Reachability for Nonlinear Systems via the Hopf Formula
Will Sharpless, Yat Tin Chow, Sylvia Herbert
https://arxiv.org/abs/2403.14184

Conservative Linear Envelopes for High-Dimensional, Hamilton-Jacobi Reachability for Nonlinear Systems via the Hopf Formula
Hamilton-Jacobi reachability (HJR) analysis provides a value function that encodes (1) the set of states from which a nonlinear system with bounded control inputs can reach a goal (or avoid a failure set) despite any bounded disturbance, and (2) the corresponding optimal control policy to reach (or avoid). Though powerful, traditional methods for HJR rely on dynamic programming and suffer from exponential computation growth with respect to state dimension. The recently favored Hopf formula miti…

Explaining Genetic Programming Trees using Large Language Models
Paula Maddigan, Andrew Lensen, Bing Xue
https://arxiv.org/abs/2403.03397 https://

Explaining Genetic Programming Trees using Large Language Models
Genetic programming (GP) has the potential to generate explainable results, especially when used for dimensionality reduction. In this research, we investigate the potential of leveraging eXplainable AI (XAI) and large language models (LLMs) like ChatGPT to improve the interpretability of GP-based non-linear dimensionality reduction. Our study introduces a novel XAI dashboard named GP4NLDR, the first approach to combine state-of-the-art GP with an LLM-powered chatbot to provide comprehensive, u…

Convergence of Some Convex Message Passing Algorithms to a Fixed Point
Vaclav Voracek, Tomas Werner
https://arxiv.org/abs/2403.07004 https://

Convergence of Some Convex Message Passing Algorithms to a Fixed Point
A popular approach to the MAP inference problem in graphical models is to minimize an upper bound obtained from a dual linear programming or Lagrangian relaxation by (block-)coordinate descent. Examples of such algorithms are max-sum diffusion and sequential tree-reweighted message passing. Convergence properties of these methods are currently not fully understood. They have been proved to converge to the set characterized by local consistency of active constraints, with unknown convergence rat…

Surface Movement Method for Linear Programming
Nikolay A. Olkhovsky, Leonid B. Sokolinsky
https://arxiv.org/abs/2404.12640 https://ar…

Surface Movement Method for Linear Programming
The article presents a new method of linear programming, called the surface movement method. This method constructs an optimal objective path on the surface of the feasible polytope from the initial boundary point to the point at which the optimal value of the objective function is achieved. The optimality of the path means moving in the direction of maximum increase/decrease in the value of the objective function. A formal description of the algorithm implementing the surface movement method i…

This https://arxiv.org/abs/2307.02551 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_qu…

Semidefinite programming relaxations for quantum correlations
Semidefinite programs are convex optimisation problems involving a linear objective function and a domain of positive semidefinite matrices. Over the last two decades, they have become an indispensable tool in quantum information science. Many otherwise intractable fundamental and applied problems can be successfully approached by means of relaxation to a semidefinite program. Here, we review such methodology in the context of quantum correlations. We discuss how the core idea of semidefinite r…

This https://arxiv.org/abs/2212.02371 has been replaced.
link: https://scholar.google.com/scholar?q=a

Integration in Cones
Measurable cones, with linear and measurable functions as morphisms, are a model of intuitionistic linear logic and of call-by-name probabilistic PCF which accommodates ``continuous data types'' such as the real line. So far however, they lacked a major feature to make them a model of more general probabilistic programming languages (notably call-by-value and call-by-push-value languages): a theory of integration for functions whose codomain is a cone, which is the key ingredient for interpreti…

This https://arxiv.org/abs/2403.08435 has been replaced.
link: https://scholar.google.com/scholar?q=a

Asymptotic behaviour of integer programming and the $\text{v}$-function of a graded filtration
The $\text{v}$-function of a graded filtration $\mathcal{I}=\{I_{[k]}\}_{k\ge0}$ is introduced. Under the assumption that $\mathcal{I}$ is Noetherian, we prove that the $\text{v}$-function $\text{v}(I_{[k]})$ is an eventually quasi-linear function. This result applies to several situations, including ordinary powers, and integral closures of ordinary powers, among others. As another application, we investigate the asymptotic behaviour of certain integer programming problems. Finally, we present…

This https://arxiv.org/abs/2311.06687 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Conditions when the problems of linear programming are algorithmically unsolvable
We study the properties of the constructive linear programing problems. The parameters of linear functions in such problems are constructive real numbers. To solve such a problem is to find the optimal plan with the constructive real number components. We show that it is impossible to have an algorithm that solves an arbitrary constructive real programming problem.

This https://arxiv.org/abs/1807.05477 has been replaced.
link: https://scholar.google.com/scholar?q=a

Linear Programming Based Near-Optimal Pricing for Laminar Bayesian Online Selection
The Bayesian online selection problem aims to design a pricing scheme for a sequence of arriving buyers that maximizes the expected social welfare (or revenue) subject to different structural constraints. Inspired by applications with a hierarchy of service, this paper focuses on the cases where a laminar matroid characterizes the set of served buyers. We give the first Polynomial-Time Approximation Scheme (PTAS) for the problem when the laminar matroid has constant depth. Our approach is based…

Convergence of Some Convex Message Passing Algorithms to a Fixed Point
Vaclav Voracek, Tomas Werner
https://arxiv.org/abs/2403.07004 https://

Convergence of Some Convex Message Passing Algorithms to a Fixed Point
A popular approach to the MAP inference problem in graphical models is to minimize an upper bound obtained from a dual linear programming or Lagrangian relaxation by (block-)coordinate descent. Examples of such algorithms are max-sum diffusion and sequential tree-reweighted message passing. Convergence properties of these methods are currently not fully understood. They have been proved to converge to the set characterized by local consistency of active constraints, with unknown convergence rat…

This https://arxiv.org/abs/2310.11760 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_ees…

Performance Investigation of an Optimal Control Strategy for Zero-Emission Operations of Shipboard Microgrids
This work introduces an efficient power management approach for shipboard microgrids that integrates diesel generators, a fuel cell, and battery energy storage system. This strategy addresses both unit commitment and power dispatch, considering the zero-emission capability of the ship, as well as optimizing the ship's speed. The optimization is done through mixed integer linear programming with the objective of minimizing the operational cost of all the power resources. Evaluations are conducte…

This https://arxiv.org/abs/2302.13616 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

ResQPASS: an algorithm for bounded variable linear least squares with asymptotic Krylov convergence
We present the Residual Quadratic Programming Active-Set Subspace (ResQPASS) method that solves large-scale linear least-squares problems with bound constraints on the variables. The problem is solved by creating a series of small problems of increasing size by projecting on the basis of residuals. Each projected problem is solved by the active-set method for convex quadratic programming, warm-started with a working set and solution of the previous problem. The method coincides with conjugate g…

This https://arxiv.org/abs/2308.06254 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csDS_…

A Better-Than-1.6-Approximation for Prize-Collecting TSP
Prize-Collecting TSP is a variant of the traveling salesperson problem where one may drop vertices from the tour at the cost of vertex-dependent penalties. The quality of a solution is then measured by adding the length of the tour and the sum of all penalties of vertices that are not visited. We present a polynomial-time approximation algorithm with an approximation guarantee slightly below $1.6$, where the guarantee is with respect to the natural linear programming relaxation of the problem. …

Lighter, Better, Faster Multi-Source Domain Adaptation with Gaussian Mixture Models and Optimal Transport
Eduardo Fernandes Montesuma, Fred Ngol\`e Mboula, Antoine Souloumiac
https://arxiv.org/abs/2404.10261

Lighter, Better, Faster Multi-Source Domain Adaptation with Gaussian Mixture Models and Optimal Transport
In this paper, we tackle Multi-Source Domain Adaptation (MSDA), a task in transfer learning where one adapts multiple heterogeneous, labeled source probability measures towards a different, unlabeled target measure. We propose a novel framework for MSDA, based on Optimal Transport (OT) and Gaussian Mixture Models (GMMs). Our framework has two key advantages. First, OT between GMMs can be solved efficiently via linear programming. Second, it provides a convenient model for supervised learning, e…

This https://arxiv.org/abs/2311.02047 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

On the Diameter of a 2-Sum of Polyhedra
The study of the combinatorial diameter of a polyhedron is a classical topic in linear-programming theory due to its close connection with the possibility of a polynomial simplex-method pivot rule. The 2-sum operation is a classical operation for graphs, matrices, and matroids; we extend this definition to polyhedra. We analyze the diameters of 2-sum polyhedra, which are those polyhedra that arise from this operation. These polyhedra appear in matroid and integer-programming theory as a natural…

This https://arxiv.org/abs/2311.01054 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csLO_…

A feasible and unitary quantum programming language
We introduce a novel quantum programming language featuring higher-order programs and quantum controlflow which ensures that all qubit transformations are unitary. Our language boasts a type system guaranteeingboth unitarity and polynomial-time normalization. Unitarity is achieved by using a special modality forsuperpositions while requiring orthogonality among superposed terms. Polynomial-time normalization isachieved using a linear-logic-based type discipline employing Barber and Plotkin dual…

This https://arxiv.org/abs/2311.02047 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

On the Diameter of a 2-Sum of Polyhedra
The study of the combinatorial diameter of a polyhedron is a classical topic in linear-programming theory due to its close connection with the possibility of a polynomial simplex-method pivot rule. The 2-sum operation is a classical operation for graphs, matrices, and matroids; we extend this definition to polyhedra. We analyze the diameters of 2-sum polyhedra, which are those polyhedra that arise from this operation. These polyhedra appear in matroid and integer-programming theory as a natural…

This https://arxiv.org/abs/2302.13616 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

ResQPASS: an algorithm for bounded variable linear least squares with asymptotic Krylov convergence
We present the Residual Quadratic Programming Active-Set Subspace (ResQPASS) method that solves large-scale linear least-squares problems with bound constraints on the variables. The problem is solved by creating a series of small problems of increasing size by projecting on the basis of residuals. Each projected problem is solved by the active-set method for convex quadratic programming, warm-started with a working set and solution of the previous problem. The method coincides with conjugate g…

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…

This https://arxiv.org/abs/2401.00778 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Convergence analysis of Lawson's iteration for the polynomial and rational minimax approximations
Lawson's iteration is a classical and effective method for solving the linear (polynomial) minimax approximation in the complex plane. Extension of Lawson's iteration for the rational minimax approximation with both computationally high efficiency and theoretical guarantee is challenging. A recent work [L.-H. Zhang, L. Yang, W. H. Yang and Y.-N. Zhang, A convex dual programming for the rational minimax approximation and Lawson's iteration, 2023, arXiv:2308.06991v1] reveals that Lawson's iterati…

This https://arxiv.org/abs/2403.16173 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

A robust optimization approach model for a multi-vaccine multi-echelon supply chain
This research investigates a multi-product, multi-echelon, and multi-period vaccine supply chain network model under uncertainty and quality inspection errors. The objective function seeks optimizing the total cost of the supply chain. Moreover, the proposed model is formulated as a mixed integer linear programming problem under multiple sources of uncertain parameters including demand, inspection errors, vaccine waste generated in healthcare centers, and defective treatment rate of vaccine was…

This https://arxiv.org/abs/2403.16173 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

A robust optimization approach model for a multi-vaccine multi-echelon supply chain
This research investigates a multi-product, multi-echelon, and multi-period vaccine supply chain network model under uncertainty and quality inspection errors. The objective function seeks optimizing the total cost of the supply chain. Moreover, the proposed model is formulated as a mixed integer linear programming problem under multiple sources of uncertain parameters including demand, inspection errors, vaccine waste generated in healthcare centers, and defective treatment rate of vaccine was…

This https://arxiv.org/abs/2210.01684 has been replaced.
link: https://scholar.google.com/scholar?q=a

Sign uncertainty principles and low-degree polynomials
We prove an asymptotically sharp version of the Bourgain-Clozel-Kahane and Cohn-Gonçalves sign uncertainty principles for polynomials of sublinear degree times a Gaussian, as the dimension tends to infinity. In particular, we show that polynomials whose degree is sublinear in the dimension cannot improve asymptotically on those of degree at most three. This question arises naturally in the study of both linear programming bounds for sphere packing and the spinless modular bootstrap bound for f…

A Low-Rank ADMM Splitting Approach for Semidefinite Programming
Qiushi Han, Chenxi Li, Zhenwei Lin, Caihua Chen, Qi Deng, Dongdong Ge, Huikang Liu, Yinyu Ye
https://arxiv.org/abs/2403.09133

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…

Randomized Nystr\"om Preconditioned Interior Point-Proximal Method of Multipliers
Ya-Chi Chu, Luiz-Rafael Santos, Madeleine Udell
https://arxiv.org/abs/2404.14524

Randomized Nyström Preconditioned Interior Point-Proximal Method of Multipliers
We present a new algorithm for convex separable quadratic programming (QP) called Nys-IP-PMM, a regularized interior-point solver that uses low-rank structure to accelerate solution of the Newton system. The algorithm combines the interior point proximal method of multipliers (IP-PMM) with the randomized Nyström preconditioned conjugate gradient method as the inner linear system solver. Our algorithm is matrix-free: it accesses the input matrices solely through matrix-vector products, as oppos…

Integer Points in Arbitrary Convex Cones: The Case of the PSD and SOC Cones
Jes\'us A. De Loera, Brittney Marsters, Luze Xu, Shixuan Zhang
https://arxiv.org/abs/2403.09927

Integer Points in Arbitrary Convex Cones: The Case of the PSD and SOC Cones
We investigate the semigroup of integer points inside a convex cone. We extend classical results in integer linear programming to integer conic programming. We show that the semigroup associated with nonpolyhedral cones can sometimes have a notion of finite generating set. We show this is true for the cone of positive semidefinite matrices (PSD) and the second-order cone (SOC). Both cones have a finite generating set of integer points, similar in spirit to Hilbert bases, under the action of a f…

This https://arxiv.org/abs/2210.01684 has been replaced.
link: https://scholar.google.com/scholar?q=a

Sign uncertainty principles and low-degree polynomials
We prove an asymptotically sharp version of the Bourgain-Clozel-Kahane and Cohn-Gonçalves sign uncertainty principles for polynomials of sublinear degree times a Gaussian, as the dimension tends to infinity. In particular, we show that polynomials whose degree is sublinear in the dimension cannot improve asymptotically on those of degree at most three. This question arises naturally in the study of both linear programming bounds for sphere packing and the spinless modular bootstrap bound for f…

This https://arxiv.org/abs/2402.03118 has been replaced.
link: https://scholar.google.com/scholar?q=a

Integrating Random Regret Minimization-Based Discrete Choice Models with Mixed Integer Linear Programming for Revenue Optimization
This paper explores the critical domain of Revenue Management (RM) within Operations Research (OR), focusing on intricate pricing dynamics. Utilizing Mixed Integer Linear Programming (MILP) models, the study enhances revenue optimization by considering product prices as decision variables and emphasizing the interplay between demand and supply. Recent advancements in Discrete Choice Models (DCMs), particularly those rooted in Random Regret Minimization (RRM) theory, are investigated as potent a…

This https://arxiv.org/abs/2206.10709 has been replaced.
link: https://scholar.google.com/scholar?q=a

PaPILO: A Parallel Presolving Library for Integer and Linear Programming with Multiprecision Support
Presolving has become an essential component of modern MIP solvers both in terms of computational performance and numerical robustness. In this paper, we present PaPILO, a new C++ header-only library that provides a large set of presolving routines for MIP and LP problems from the literature. The creation of PaPILO was motivated by the current lack of (a) solver-independent implementations that (b) exploit parallel hardware, and (c) support multiprecision arithmetic. Traditionally, presolving i…

This https://arxiv.org/abs/2401.09277 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Certifying MIP-based Presolve Reductions for 0-1 Integer Linear Programs
It is well known that reformulating the original problem can be crucial for the performance of mixed-integer programming (MIP) solvers. To ensure correctness, all transformations must preserve the fea sibility status and optimal value of the problem, but there is currently no established methodology to express and verify the equivalence of two mixed-integer programs. In this work, we take a first step in this direction by showing how the correctness of MIP presolve reductions on 0-1 integer lin…

This https://arxiv.org/abs/2304.01343 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

A study of distributionally robust mixed-integer programming with Wasserstein metric: on the value of incomplete data
This study addresses a class of linear mixed-integer programming (MILP) problems that involve uncertainty in the objective function parameters. The parameters are assumed to form a random vector, whose probability distribution can only be observed through a finite training data set. Unlike most of the related studies in the literature, we also consider uncertainty in the underlying data set. The data uncertainty is described by a set of linear constraints for each random sample, and the uncerta…

Optimal control of continuous-time symmetric systems with unknown dynamics and noisy measurements
Hamed Taghavian, Florian Dorfler, Mikael Johansson
https://arxiv.org/abs/2403.13605

Optimal control of continuous-time symmetric systems with unknown dynamics and noisy measurements
An iterative learning algorithm is presented for continuous-time linear-quadratic optimal control problems where the system is externally symmetric with unknown dynamics. Both finite-horizon and infinite-horizon problems are considered. It is shown that the proposed algorithm is globally convergent to the optimal solution and has some advantages over adaptive dynamic programming, including being unbiased under noisy measurements and having a relatively low computational burden. Numerical experi…

This https://arxiv.org/abs/2308.15805 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Design of Coherent Passive Quantum Equalizers Using Robust Control Theory
The paper develops a methodology for the design of coherent equalizing filters for quantum communication channels. Given a linear quantum system model of a quantum communication channel, the aim is to obtain another quantum system which, when coupled with the original system, mitigates degrading effects of the environment. The main result of the paper is a systematic equalizer synthesis algorithm which relies on methods of state-space robust control design via semidefinite programming.

This https://arxiv.org/abs/2311.07710 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

A Practical and Optimal First-Order Method for Large-Scale Convex Quadratic Programming
Convex quadratic programming (QP) is an important class of optimization problem with wide applications in practice. The classic QP solvers are based on either simplex or barrier method, both of which suffer from the scalability issue because their computational bottleneck is solving linear equations. In this paper, we design and analyze a first-order method for QP, called restarted accelerated primal-dual hybrid gradient (rAPDHG), whose computational bottleneck is matrix-vector multiplication. …

Maximizing Slice-Volumes of Semialgebraic Sets using Sum-of-Squares Programming
Jared Miller, Chiara Meroni, Matteo Tacchi, Mauricio Velasco
https://arxiv.org/abs/2403.04438

Maximizing Slice-Volumes of Semialgebraic Sets using Sum-of-Squares Programming
This paper presents an algorithm to maximize the volume of an affine slice through a given semialgebraic set. This slice-volume task is formulated as an infinite-dimensional linear program in continuous functions, inspired by prior work in volume computation of semialgebraic sets. A convergent sequence of upper-bounds to the maximal slice volume are computed using the moment-Sum-of-Squares hierarchy of semidefinite programs in increasing size. The computational complexity of this scheme can be …

Zero-Sum Games for Volterra Integral Equations and Viscosity Solutions of Path-Dependent Hamilton-Jacobi Equations
Mikhail I. Gomoyunov
https://arxiv.org/abs/2404.10428

Zero-Sum Games for Volterra Integral Equations and Viscosity Solutions of Path-Dependent Hamilton-Jacobi Equations
We consider a game, in which the dynamics is described by a non-linear Volterra integral equation of Hammerstein type with a weakly-singular kernel and the goals of the first and second players are, respectively, to minimize and maximize a given cost functional. We propose a way of how the dynamic programming principle can be formalized and the theory of generalized (viscosity) solutions of path-dependent Hamilton--Jacobi equations can be developed in order to prove the existence of the game va…

On Integer Programs with Irrational Data
Seyedmohammadhossein Hosseinian, Andrew J. Schaefer
https://arxiv.org/abs/2402.07117 https://

On Integer Programs with Irrational Data
An integer program (IP) with a finite number of feasible solutions may have an unbounded linear programming relaxation if it contains irrational parameters, due to implicit constraints enforced by the irrational numbers. We show that those constraints can be obtained if the irrational parameters are polynomials of roots of integers over the field of rational numbers, leading to an equivalent rational formulation. We also establish a weaker result for IPs involving the general class of algebraic…

This https://arxiv.org/abs/2404.04158 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Hardness of circuit and monotone diameters of polytopes
The Circuit diameter of polytopes was introduced by Borgwardt, Finhold and Hemmecke as a fundamental tool for the study of circuit augmentation schemes for linear programming and for estimating combinatorial diameters. Determining the complexity of computing the circuit diameter of polytopes was posed as an open problem by Sanità as well as by Kafer, and was recently reiterated by Borgwardt, Grewe, Kafer, Lee and Sanità. In this paper, we solve this problem by showing that computing the cir…

This https://arxiv.org/abs/2404.04158 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Hardness of circuit and monotone diameters of polytopes
The Circuit diameter of polytopes was introduced by Borgwardt, Finhold and Hemmecke as a fundamental tool for the study of circuit augmentation schemes for linear programming and for estimating combinatorial diameters. Determining the complexity of computing the circuit diameter of polytopes was posed as an open problem by Sanità as well as by Kafer, and was recently reiterated by Borgwardt, Grewe, Kafer, Lee and Sanità. In this paper, we solve this problem by showing that computing the cir…

The circle packing problem: a theoretical comparison of various convexification techniques
Aida Khajavirad
https://arxiv.org/abs/2404.03091 https://…

The circle packing problem: a theoretical comparison of various convexification techniques
We consider the problem of packing congruent circles with the maximum radius in a unit square as a mathematical optimization problem. Due to the presence of non-overlapping constraints, this problem is a notoriously difficult nonconvex quadratically constrained optimization problem, which possesses many local optima. We consider several popular convexification techniques, giving rise to linear programming relaxations and semidefinite programming relaxations for the circle packing problem. We co…

Aggregation of pairwise comparison matrices: A clustering approach
Kolos Csaba \'Agoston, S\'andor Boz\'oki, L\'aszl\'o Csat\'o
https://arxiv.org/abs/2402.06061

Aggregation of pairwise comparison matrices: A clustering approach
We consider clustering in group decision making where the opinions are given by pairwise comparison matrices. In particular, the k-medoids model is suggested to classify the matrices as it has a linear programming problem formulation. Its objective function depends on the measure of dissimilarity between the matrices but not on the weights derived from them. With one cluster, our methodology provides an alternative to the conventional aggregation procedures. It can also be used to quantify the …

This https://arxiv.org/abs/2401.03838 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

A hybrid metaheuristic to optimize electric first-mile feeder services with charging synchronization constraints and customer rejections
This paper addresses the on-demand meeting-point-based feeder electric bus routing and charging scheduling problem under charging synchronization constraints. The problem considered exhibits the structure of the location routing problem, which is more difficult to solve than many electric vehicle routing problems with capacitated charging stations. We propose to model the problem using a mixed-integer linear programming approach based on a layered graph structure. An efficient hybrid metaheuris…

This https://arxiv.org/abs/2402.01066 has been replaced.
link: https://scholar.google.com/scholar?q=a

On the Hardness of Short and Sign-Compatible Circuit Walks
The circuits of a polyhedron are a superset of its edge directions. Circuit walks, a sequence of steps along circuits, generalize edge walks and are "short" if they have few steps or small total length. Both interpretations of short are relevant to the theory and application of linear programming. We study the hardness of several problems relating to the construction of short circuit walks. We establish that for a pair of vertices of a $0/1$-network-flow polytope, it is NP-complete to determi…

Inexact Policy Iteration Methods for Large-Scale Markov Decision Processes
Matilde Gargiani, Robin Sieber, Efe Balta, Dominic Liao-McPherson, John Lygeros
https://arxiv.org/abs/2404.06136

Inexact Policy Iteration Methods for Large-Scale Markov Decision Processes
We consider inexact policy iteration methods for large-scale infinite-horizon discounted MDPs with finite spaces, a variant of policy iteration where the policy evaluation step is implemented inexactly using an iterative solver for linear systems. In the classical dynamic programming literature, a similar principle is deployed in optimistic policy iteration, where an a-priori fixed-number of iterations of value iteration is used to inexactly solve the policy evaluation step. Inspired by the con…

Hardness of circuit and monotone diameters of polytopes
Christian N\"obel, Raphael Steiner
https://arxiv.org/abs/2404.04158 https://

Hardness of circuit and monotone diameters of polytopes
The Circuit diameter of polytopes was introduced by Borgwardt, Finhold and Hemmecke as a fundamental tool for the study of circuit augmentation schemes for linear programming and for estimating combinatorial diameters. Determining the complexity of computing the circuit diameter of polytopes was posed as an open problem by Sanità as well as by Kafer, and was recently reiterated by Borgwardt, Grewe, Kafer, Lee and Sanità. In this paper, we solve this problem by showing that computing the cir…