Tootfinder

ASP-FZN: A Translation-based Constraint Answer Set Solver
Thomas Eiter, Tobias Geibinger, Tobias Kaminski, Nysret Musliu, Johannes Oetsch
https://arxiv.org/abs/2507.22774 https:…

ASP-FZN: A Translation-based Constraint Answer Set Solver
We present the solver asp-fzn for Constraint Answer Set Programming (CASP), which extends ASP with linear constraints. Our approach is based on translating CASP programs into the solver-independent FlatZinc language that supports several Constraint Programming and Integer Programming backend solvers. Our solver supports a rich language of linear constraints, including some common global constraints. As for evaluation, we show that asp-fzn is competitive with state-of-the-art ASP solvers on benc…

FMIP: Multimodal Flow Matching for Mixed Integer Linear Programming
Hongpei Li, Hui Yuan, Han Zhang, Dongdong Ge, Mengdi Wang, Yinyu Ye
https://arxiv.org/abs/2507.23390 https://…

FMIP: Multimodal Flow Matching for Mixed Integer Linear Programming
Mixed-Integer Linear Programming (MILP) is a cornerstone of mathematical optimization, enabling the modeling of complex decision-making problems involving both integer and continuous variables. Despite its versatility, most MILP problems are NP-complete, making them challenging to solve in practice. Existing graph neural network (GNN)-based heuristics aim to reduce problem scale by predicting only the solutions on integer variables for a given instance, struggling to capture the intricate inter…

Leveraging machine learning features for linear optical interferometer control
Sergei S. Kuzmin, Ivan V. Dyakonov, Stanislav S. Straupe
https://arxiv.org/abs/2505.24032

Leveraging machine learning features for linear optical interferometer control
We have developed an algorithm that constructs a model of a reconfigurable optical interferometer, independent of specific architectural constraints. The programming of unitary transformations on the interferometer's optical modes relies on either an analytical method for deriving the unitary matrix from a set of phase shifts or an optimization routine when such decomposition is not available. Our algorithm employs a supervised learning approach, aligning the interferometer model with a trainin…

Incremental Gain Computation and Regulation of Discrete-time Positive Lur\'e Systems using Linear Programming
Jared Miller
https://arxiv.org/abs/2505.24386

Incremental Gain Computation and Regulation of Discrete-time Positive Luré Systems using Linear Programming
This work approaches the problem of computing incremental $\ell_1$ and $\ell_\infty$ gains for discrete-time positive systems in \lure feedback with static memoryless nonlinearities, and regulating the $\ell_\infty$ gain through the design of a state-feedback controller. Finite incremental gains provide a quantitative measure of robustness for trajectories, and will ensure that all pairs of trajectories will converge to a fixed point or will diverge together in the absence of an applied input. …

Linear programming bounds in homogeneous spaces, I: Optimal packing density
Maximilian Wackenhuth
https://arxiv.org/abs/2505.23572 https://

Linear programming bounds in homogeneous spaces, I: Optimal packing density
In this article we obtain linear programming bounds for the maximal sphere packing density of commutative spaces. A special case of our results solves a conjecture by Cohn and Zhao on linear programming bounds for sphere packings in hyperbolic space.

Thread and Memory-Safe Programming with CLASS
Lu\'is Caires (Instituto Superior T\'ecnico)
https://arxiv.org/abs/2505.20848 https://

Thread and Memory-Safe Programming with CLASS
CLASS is a proof-of-concept general purpose linear programming language, flexibly supporting realistic concurrent programming idioms, and featuring an expressive linear type system ensuring that programs (1) never misuse or leak stateful resources or memory, (2) never deadlock, and (3) always terminate. The design of CLASS and the strong static guarantees of its type system originates in its Linear Logic and proposition-as-types foundations. However, instead of focusing on its theoretical found…

Global Predecessor Indexing: Avoiding Binary Search in Weighted Job Scheduling
Amit Joshi
https://arxiv.org/abs/2506.22922 https://ar…

Global Predecessor Indexing: Avoiding Binary Search in Weighted Job Scheduling
We present an improved solution to the Weighted Job Scheduling (WJS) problem. While the classical dynamic programming (DP) solution runs in $O(n \log(n))$ time due to comparison-based sorting and per-job binary search, we eliminate the binary search bottleneck. In its place, we introduce a novel multi-phase preprocessing technique called Global Predecessor Indexing (GPI), which computes the latest non-overlapping job (i.e., the predecessor) for all jobs via a two-pointer linear-time pass. GPI e…

Solving a real-world modular logistic scheduling problem with a quantum-classical metaheuristics
Florian Krellner, Abhishek Awasthi, Nico Kraus, Sarah Braun, Michael Poppel, Daniel Porawski
https://arxiv.org/abs/2507.21701

Solving a real-world modular logistic scheduling problem with a quantum-classical metaheuristics
This study evaluates the performance of a quantum-classical metaheuristic and a traditional classical mathematical programming solver, applied to two mathematical optimization models for an industry-relevant scheduling problem with autonomous guided vehicles (AGVs). The two models are: (1) a time-indexed mixed-integer linear program, and (2) a novel binary optimization problem with linear and quadratic constraints and a linear objective. Our experiments indicate that optimization methods are ve…

Binary Classification with the Maximum Score Model and Linear Programming
Joel L. Horowitz, Sokbae Lee
https://arxiv.org/abs/2507.19654 https://arxiv.org/p…

Binary Classification with the Maximum Score Model and Linear Programming
This paper presents a computationally efficient method for binary classification using Manski's (1975,1985) maximum score model when covariates are discretely distributed and parameters are partially but not point identified. We establish conditions under which it is minimax optimal to allow for either non-classification or random classification and derive finite-sample and asymptotic lower bounds on the probability of correct classification. We also describe an extension of our method to conti…

On the $l_\infty$-analog of Algebraic Connectivity
M. Rajesh Kannan, Rahul Roy
https://arxiv.org/abs/2507.22015 https://arxiv.org/pdf/2507.22015

On the $l_\infty$-analog of Algebraic Connectivity
The algebraic connectivity $a(G)$ of a graph $G$ is defined as the second smallest eigenvalue of its Laplacian matrix $L(G)$. It also admits a variational characterization as the minimum of a quadratic form associated with $L(G)$, subject to $l_2$-norm constraints. In 2024, Andrade and Dahl investigated an analogous parameter $γ(G)$, defined using the $l_\infty$-norm instead of the $l_2$-norm. They demonstrated that $γ(G)$ can be computed in polynomial time using linear programming. In this a…

Symbolically Regressing Fish Biomass Spectral Data: A Linear Genetic Programming Method with Tunable Primitives
Zhixing Huang, Bing Xue, Mengjie Zhang, Jeremy S. Ronney, Keith C. Gordon, Daniel P. Killeen
https://arxiv.org/abs/2505.21901

Symbolically Regressing Fish Biomass Spectral Data: A Linear Genetic Programming Method with Tunable Primitives
Machine learning techniques play an important role in analyzing spectral data. The spectral data of fish biomass is useful in fish production, as it carries many important chemistry properties of fish meat. However, it is challenging for existing machine learning techniques to comprehensively discover hidden patterns from fish biomass spectral data since the spectral data often have a lot of noises while the training data are quite limited. To better analyze fish biomass spectral data, this pap…

Convex Approximations of Random Constrained Markov Decision Processes
V Varagapriya, Vikas Vikram Singh, Abdel Lisser
https://arxiv.org/abs/2505.24815 http…

Convex Approximations of Random Constrained Markov Decision Processes
Constrained Markov decision processes (CMDPs) are used as a decision-making framework to study the long-run performance of a stochastic system. It is well-known that a stationary optimal policy of a CMDP problem under discounted cost criterion can be obtained by solving a linear programming problem when running costs and transition probabilities are exactly known. In this paper, we consider a discounted cost CMDP problem where the running costs and transition probabilities are defined using ran…

Symbolically Regressing Fish Biomass Spectral Data: A Linear Genetic Programming Method with Tunable Primitives
Zhixing Huang, Bing Xue, Mengjie Zhang, Jeremy S. Ronney, Keith C. Gordon, Daniel P. Killeen
https://arxiv.org/abs/2505.21901

Symbolically Regressing Fish Biomass Spectral Data: A Linear Genetic Programming Method with Tunable Primitives
Machine learning techniques play an important role in analyzing spectral data. The spectral data of fish biomass is useful in fish production, as it carries many important chemistry properties of fish meat. However, it is challenging for existing machine learning techniques to comprehensively discover hidden patterns from fish biomass spectral data since the spectral data often have a lot of noises while the training data are quite limited. To better analyze fish biomass spectral data, this pap…

An Explainable Equity-Aware P2P Energy Trading Framework for Socio-Economically Diverse Microgrid
Abhijan Theja, Mayukha Pal
https://arxiv.org/abs/2507.18738 https://

An Explainable Equity-Aware P2P Energy Trading Framework for Socio-Economically Diverse Microgrid
Fair and dynamic energy allocation in community microgrids remains a critical challenge, particularly when serving socio-economically diverse participants. Static optimization and cost-sharing methods often fail to adapt to evolving inequities, leading to participant dissatisfaction and unsustainable cooperation. This paper proposes a novel framework that integrates multi-objective mixed-integer linear programming (MILP), cooperative game theory, and a dynamic equity-adjustment mechanism driven…

Iterative Vickrey Auctions via Linear Programming
S\'ebastien Lahaie, Benjamin Lubin
https://arxiv.org/abs/2507.03252 https://arx…

Iterative Vickrey Auctions via Linear Programming
Building on the linear programming approach to competitive equilibrium pricing, we develop a general method for constructing iterative auctions that achieve Vickrey-Clarke-Groves (VCG) outcomes. We show how to transform a linear program characterizing competitive equilibrium prices into one that characterizes universal competitive equilibrium (UCE) prices, which elicit precisely the information needed to compute VCG payments. By applying a primal-dual algorithm to these transformed programs, we…

Bridging Fitness With Search Spaces By Fitness Supremums: A Theoretical Study on LGP
Zhixing Huang, Yi Mei, Fangfang Zhang, Mengjie Zhang, Wolfgang Banzhaf
https://arxiv.org/abs/2505.21991

Bridging Fitness With Search Spaces By Fitness Supremums: A Theoretical Study on LGP
Genetic programming has undergone rapid development in recent years. However, theoretical studies of genetic programming are far behind. One of the major obstacles to theoretical studies is the challenge of developing a model to describe the relationship between fitness values and program genotypes. In this paper, we take linear genetic programming (LGP) as an example to study the fitness-to-genotype relationship. We find that the fitness expectation increases with fitness supremum over instruc…

Efficient Learning of Balanced Signed Graphs via Sparse Linear Programming
Haruki Yokota, Hiroshi Higashi, Yuichi Tanaka, Gene Cheung
https://arxiv.org/abs/2506.01826

Efficient Learning of Balanced Signed Graphs via Sparse Linear Programming
Signed graphs are equipped with both positive and negative edge weights, encoding pairwise correlations as well as anti-correlations in data. A balanced signed graph is a signed graph with no cycles containing an odd number of negative edges. Laplacian of a balanced signed graph has eigenvectors that map via a simple linear transform to ones in a corresponding positive graph Laplacian, thus enabling reuse of spectral filtering tools designed for positive graphs. We propose an efficient method t…

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 …

Eigenvalue bounds for distance-edge colorings
Aida Abiad, Luuk Reijnders
https://arxiv.org/abs/2506.20976 https://arxiv.org/pdf/2506.…

Eigenvalue bounds for distance-edge colorings
For a fixed positive integer $t$, we consider the graph colouring problem in which edges at distance at most $t$ are given distinct colours. We obtain sharp lower bounds for the distance-$t$ chromatic index, the least number of colours necessary for such a colouring. Our bounds are of algebraic nature; they depend on the eigenvalues of the line graph and on a polynomial which can be found using integer linear programming methods. We show several graph classes that attain equality for our bounds…

AI for the Routine, Humans for the Complex: Accuracy-Driven Data Labelling with Mixed Integer Linear Programming
Mohammad Hossein Amini, Mehrdad Sabetzadeh, Shiva Nejati
https://arxiv.org/abs/2507.04990

AI for the Routine, Humans for the Complex: Accuracy-Driven Data Labelling with Mixed Integer Linear Programming
The scarcity of accurately labelled data remains a major challenge in deep learning (DL). Many DL approaches rely on semi-supervised methods, which focus on constructing large datasets that require only a minimal amount of human-labelled data. Since DL training algorithms can tolerate moderate label noise, it has generally been acceptable for the accuracy of labels in large training datasets to fall well short of a perfect 100%. However, when it comes to testing DL models, achieving high label …

The Emergence of Deep Reinforcement Learning for Path Planning
Thanh Thi Nguyen, Saeid Nahavandi, Imran Razzak, Dung Nguyen, Nhat Truong Pham, Quoc Viet Hung Nguyen
https://arxiv.org/abs/2507.15469

The Emergence of Deep Reinforcement Learning for Path Planning
The increasing demand for autonomous systems in complex and dynamic environments has driven significant research into intelligent path planning methodologies. For decades, graph-based search algorithms, linear programming techniques, and evolutionary computation methods have served as foundational approaches in this domain. Recently, deep reinforcement learning (DRL) has emerged as a powerful method for enabling autonomous agents to learn optimal navigation strategies through interaction with t…

Enhanced PDHG for Linear Programming with Online Preconditioning
Haihao Lu, Wanyu Zhang
https://arxiv.org/abs/2506.17650 https://arxi…

Enhanced PDHG for Linear Programming with Online Preconditioning
We present an online preconditioning technique for the primal-dual hybrid gradient (PDHG) algorithm for linear programming (LP). The method adaptively updates primal and dual preconditioners using an online optimization framework. To improve its practical performance, we introduce several algorithmic enhancements, including using normalized online loss functions and updating preconditioners infrequently. We implement the technique on top of vanilla PDHG and the GPU-based LP solver cuPDLP.jl, an…

Multipass Linear Sketches for Geometric LP-Type Problems
N. Efe \c{C}ekirge, William Gay, David P. Woodruff
https://arxiv.org/abs/2507.11484 https://

Multipass Linear Sketches for Geometric LP-Type Problems
LP-type problems such as the Minimum Enclosing Ball (MEB), Linear Support Vector Machine (SVM), Linear Programming (LP), and Semidefinite Programming (SDP) are fundamental combinatorial optimization problems, with many important applications in machine learning applications such as classification, bioinformatics, and noisy learning. We study LP-type problems in several streaming and distributed big data models, giving $\varepsilon$-approximation linear sketching algorithms with a focus on the h…

Bridging Fitness With Search Spaces By Fitness Supremums: A Theoretical Study on LGP
Zhixing Huang, Yi Mei, Fangfang Zhang, Mengjie Zhang, Wolfgang Banzhaf
https://arxiv.org/abs/2505.21991

Bridging Fitness With Search Spaces By Fitness Supremums: A Theoretical Study on LGP
Genetic programming has undergone rapid development in recent years. However, theoretical studies of genetic programming are far behind. One of the major obstacles to theoretical studies is the challenge of developing a model to describe the relationship between fitness values and program genotypes. In this paper, we take linear genetic programming (LGP) as an example to study the fitness-to-genotype relationship. We find that the fitness expectation increases with fitness supremum over instruc…

An Expansion-Based Approach for Quantified Integer Programming
Michael Hartisch, Leroy Chew
https://arxiv.org/abs/2506.04452 https://…

An Expansion-Based Approach for Quantified Integer Programming
Quantified Integer Programming (QIP) bridges multiple domains by extending Quantified Boolean Formulas (QBF) to incorporate general integer variables and linear constraints while also generalizing Integer Programming through variable quantification. As a special case of Quantified Constraint Satisfaction Problems (QCSP), QIP provides a versatile framework for addressing complex decision-making scenarios. Additionally, the inclusion of a linear objective function enables QIP to effectively model…

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…

Solving nonconvex Hamilton--Jacobi--Isaacs equations with PINN-based policy iteration
Hee Jun Yang, Min Jung Kim, Yeoneung Kim
https://arxiv.org/abs/2507.15455

Solving nonconvex Hamilton--Jacobi--Isaacs equations with PINN-based policy iteration
We propose a mesh-free policy iteration framework that combines classical dynamic programming with physics-informed neural networks (PINNs) to solve high-dimensional, nonconvex Hamilton--Jacobi--Isaacs (HJI) equations arising in stochastic differential games and robust control. The method alternates between solving linear second-order PDEs under fixed feedback policies and updating the controls via pointwise minimax optimization using automatic differentiation. Under standard Lipschitz and unif…

Warm-starting Strategies in Scalarization Methods for Multi-Objective Optimization
Stephanie Riedm\"uller (Zuse Institute Berlin), Janina Zittel (Zuse Institute Berlin), Thorsten Koch (Zuse Institute Berlin, Technische Universit\"at Berlin)
https://arxiv.org/abs/2507.21933

Warm-starting Strategies in Scalarization Methods for Multi-Objective Optimization
We explore how warm-starting strategies can be integrated into scalarization-based approaches for multi-objective optimization in (mixed) integer linear programming. Scalarization methods remain widely used classical techniques to compute Pareto-optimal solutions in applied settings. They are favored due to their algorithmic simplicity and broad applicability across continuous and integer programs with an arbitrary number of objectives. While warm-starting has been applied in this context befor…

Chemical Control for the Morphogenesis of Conducting Polymer Dendrites in Water
Antoine Baron, Corentin Scholaert, David Gu\'erin, Yannick Coffinier, Fabien Alibart, S\'ebastien Pecqueur
https://arxiv.org/abs/2507.16626

Chemical Control for the Morphogenesis of Conducting Polymer Dendrites in Water
Conducting polymer dendrite (CPD) morphogenesis is an electrochemical process that unlocks the potential to implement in materio evolving intelligence in electrical systems: As an electronic device experiences transient voltages in an open-space wet environment, electrically conductive structures physically change over time, programming the filtering properties of an interconnect as a non-linear analog device. Mimicking the self-preservation strategies of some sessile organisms, CPDs adapt thei…

Optimal Integration Of Heat-Pump And Solar Thermal Energy In The Pre-heating Loop Of Wood And Gas Boiler Based District Heating System
Hamza Mettali (CETHIL,INSA Lyon,AIS), Rousset Fran\c{c}ois (CETHIL), Eric Bideaux (AIS), Clausse Marc (CETHIL)
https://arxiv.org/abs/2507.18204

Optimal Integration Of Heat-Pump And Solar Thermal Energy In The Pre-heating Loop Of Wood And Gas Boiler Based District Heating System
The integration of renewable sources is essential for decarbonizing heat production in district energy networks. Beyond biomass-based solutions, solar thermal energy, with or without heat pumps, presents a significant opportunity. However, system performance is highly dependent on outdoor and setpoint temperatures. This study aims to optimize system design using a multi-criteria approach that considers techno-economic and environmental (CO2) factors. A Mixed-Integer Linear Programming (MILP) mo…

cuPDLP : A Further Enhanced GPU-Based First-Order Solver for Linear Programming
Haihao Lu, Zedong Peng, Jinwen Yang
https://arxiv.org/abs/2507.14051 https:…

cuPDLP+: A Further Enhanced GPU-Based First-Order Solver for Linear Programming
We introduce cuPDLP+, a further enhanced GPU-based first-order solver for linear programming. Building on the predecessor cuPDLP, cuPDLP+ incorporates recent algorithmic advances, including the restarted Halpern PDHG method with reflection, a novel restart criterion, and a PID-controlled primal weight update. These innovations are carefully tailored for GPU architectures and deliver substantial empirical gains. On a comprehensive benchmark of MIPLIB LP relaxations, cuPDLP+ achieves 2x - 4x spee…

This https://arxiv.org/abs/2408.15377 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csCC_…

On Approximability of Satisfiable k-CSPs: V
We propose a framework of algorithm vs. hardness for all Max-CSPs and demonstrate it for a large class of predicates. This framework extends the work of Raghavendra [STOC, 2008], who showed a similar result for almost satisfiable Max-CSPs. Our framework is based on a new hybrid approximation algorithm, which uses a combination of the Gaussian elimination technique (i.e., solving a system of linear equations over an Abelian group) and the semidefinite programming relaxation. We complement our …

Optimal Control of Hybrid Systems via Measure Relaxations
Etienne Buehrle, \"Omer \c{S}ahin Ta\c{s}, Christoph Stiller
https://arxiv.org/abs/2507.19210 https://

Optimal Control of Hybrid Systems via Measure Relaxations
We propose an approach to trajectory optimization for piecewise polynomial systems based on the recently proposed graphs of convex sets framework. We instantiate the framework with a convex relaxation of optimal control based on occupation measures, resulting in a convex optimization problem resembling the discrete shortest-paths linear program that can be solved efficiently to global optimality. While this approach inherits the limitations of semidefinite programming, scalability to large numb…

This https://arxiv.org/abs/2503.16052 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csGT_…

A Linear Programming Approach to the Super-Stable Roommates Problem
The stable roommates problem is a non-bipartite version of the well-known stable matching problem. Teo and Sethuraman proved that, for each instance of the stable roommates problem in a complete graph, there exists a linear inequality system such that there exists a feasible solution to this system if and only if there exists a stable matching in the given instance. The aim of this paper is to extend the result of Teo and Sethuraman to the stable roommates problem with ties. More concretely, we…

A polynomial delay algorithm generating all potential maximal cliques in triconnected planar graphs
Alexander Grigoriev, Yasuaki Kobayashi, Hisao Tamaki, Tom C. van der Zanden
https://arxiv.org/abs/2506.12635

A polynomial delay algorithm generating all potential maximal cliques in triconnected planar graphs
We develop a new characterization of potential maximal cliques of a triconnected planar graph and, using this characterization, give a polynomial delay algorithm generating all potential maximal cliques of a given triconnected planar graph. Combined with the dynamic programming algorithms due to Bouchitt{é} and Todinca, this algorithm leads to a treewidth algorithm for general planar graphs that runs in time linear in the number of potential maximal cliques and polynomial in the number of vert…

Tensor-Tensor Products, Group Representations, and Semidefinite Programming
Alex Dunbar, Elizabeth Newman
https://arxiv.org/abs/2507.12729 https://

Tensor-Tensor Products, Group Representations, and Semidefinite Programming
The $\star_M$-family of tensor-tensor products is a framework which generalizes many properties from linear algebra to third order tensors. Here, we investigate positive semidefiniteness and semidefinite programming under the $\star_M$-product. Critical to our investigation is a connection between the choice of matrix M in the $\star_M$-product and the representation theory of an underlying group action. Using this framework, third order tensors equipped with the $\star_M$-product are a natural…

Convergence of linear programming hierarchies for Gibbs states of spin systems
Hamza Fawzi, Omar Fawzi
https://arxiv.org/abs/2506.06125 https://

Convergence of linear programming hierarchies for Gibbs states of spin systems
We consider the problem of computing expectation values of local functions under the Gibbs distribution of a spin system. In particular, we study two families of linear programming hierarchies for this problem. The first hierarchy imposes local spin flip equalities and has been considered in the bootstrap literature in high energy physics. For this hierarchy, we prove fast convergence under a spatial mixing (decay of correlations) condition. This condition is satisfied for example above the cri…

Combinatorial Algorithm for Tropical Linearly Factorized Programming
Yuki Nishida
https://arxiv.org/abs/2507.07596 https://arxiv.org/…

Combinatorial Algorithm for Tropical Linearly Factorized Programming
The tropical semiring is a set of numbers $\mathbb{R}\cup\{-\infty\}$ with addition $a\oplus b:=\max(a,b)$ and multiplication $a\otimes b:=a+b$. As well as in conventional algebra, linear programming problem in the tropical semiring has been developed. In this study, we introduce a new type of tropical optimization problem, namely, tropical linearly factorized programming problem. This problem involves minimizing the objective function given by the product of tropical linear forms $c_{k,1}\otim…

A Newton Augmented Lagrangian Method for Symmetric Cone Programming with Complexity Analysis
Rui-Jin Zhang, Ruoyu Diao, Xin-Wei Liu, Yu-Hong Dai
https://arxiv.org/abs/2506.04802

A Newton Augmented Lagrangian Method for Symmetric Cone Programming with Complexity Analysis
Symmetric cone programming incorporates a broad class of convex optimization problems, including linear programming, second-order cone programming, and semidefinite programming. Although the augmented Lagrangian method (ALM) is well-suited for large-scale scenarios, its subproblems are often not second-order continuously differentiable, preventing direct use of classical Newton methods. To address this issue, we observe that barrier functions from interior-point methods (IPMs) naturally serve a…

The LQR-Schr\"odinger Bridge
Marc Lambert (SIERRA)
https://arxiv.org/abs/2506.17273 https://arxiv.org/pdf/2506.17273

The LQR-Schrödinger Bridge
We consider the Schr{ö}dinger bridge problem in discrete time, where the pathwise cost is replaced by a sum of quadratic functions, taking the form of a linear quadratic regulator (LQR) cost. This cost comprises potential terms that act as attractors and kinetic terms that control the diffusion of the process. When the two boundary marginals are Gaussian, we show that the LQR-Schr{ö}dinger bridge problem can be solved in closed form. We follow the dynamic programming principle, interpreting t…

On Sketching Trimmed Statistics
Honghao Lin, Hoai-An Nguyen, David P. Woodruff
https://arxiv.org/abs/2506.07342 https://arxiv.org/pdf…

On Sketching Trimmed Statistics
We present space-efficient linear sketches for estimating trimmed statistics of an $n$-dimensional frequency vector $x$, e.g., the sum of $p$-th powers of the largest $k$ frequencies (i.e., entries) in absolute value, or the $k$-trimmed vector, which excludes the top and bottom $k$ frequencies. This is called the $F_p$ moment of the trimmed vector. Trimmed measures are used in robust estimation, as seen in the R programming language's `trim.var' function and the `trim' parameter in the mean fun…

An Overview of GPU-based First-Order Methods for Linear Programming and Extensions
Haihao Lu, Jinwen Yang
https://arxiv.org/abs/2506.02174 https://

An Overview of GPU-based First-Order Methods for Linear Programming and Extensions
The rapid progress in GPU computing has revolutionized many fields, yet its potential in mathematical programming, such as linear programming (LP), has only recently begun to be realized. This survey aims to provide a comprehensive overview of recent advancements in GPU-based first-order methods for LP, with a particular focus on the design and development of cuPDLP. We begin by presenting the design principles and algorithmic foundation of the primal-dual hybrid gradient (PDHG) method, which f…

This https://arxiv.org/abs/2502.13697 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Linear programming for finite-horizon vector-valued Markov decision processes
We propose a vector linear programming formulation for a non-stationary, finite-horizon Markov decision process with vector-valued rewards. Pareto efficient policies are shown to correspond to efficient solutions of the linear program, and vector linear programming theory allows us to fully characterize deterministic efficient policies. An algorithm for enumerating all efficient deterministic policies is presented then tested numerically in an engineering application.

Price Aware Power Split Control in Heterogeneous Battery Storage Systems
Sheng Yin, Vivek Teja Tanjavooru, Thomas Hamacher, Christoph Goebel, Holger Hesse
https://arxiv.org/abs/2507.00628

Price Aware Power Split Control in Heterogeneous Battery Storage Systems
This paper presents a unified framework for the optimal scheduling of battery dispatch and internal power allocation in Battery energy storage systems (BESS). This novel approach integrates both market-based (price-aware) signals and physical system constraints to simultaneously optimize (1) external energy dispatch and (2) internal heterogeneity management of BESS, enhancing its operational economic value and performance. This work compares both model-based Linear Programming (LP) and model-fr…

On the Linear Programming Model for Dynamic Stochastic Matching and Its Application on Pricing
Junlin Chen, Chiwei Yan, Hai Jiang
https://arxiv.org/abs/2506.09924

On the Linear Programming Model for Dynamic Stochastic Matching and Its Application on Pricing
Important pricing problems in centralized matching markets -- such as carpooling and food delivery platforms -- often exhibit a bi-level structure. At the upper level, the platform sets prices for different types of agents (e.g., riders with various origins and destinations, or delivery orders from diverse restaurants to customer locations). The lower level then matches converted agents to minimize operational costs, such as pooling riders with similar itineraries into the same vehicle or conso…

Non-Euclidean dual gradient ascent for entropically regularized linear and semidefinite programming
Yuhang Cai, Michael Lindsey
https://arxiv.org/abs/2506.09711

Non-Euclidean dual gradient ascent for entropically regularized linear and semidefinite programming
We present an optimization framework that exhibits dimension-independent convergence on a broad class of semidefinite programs (SDPs). Our approach first regularizes the primal problem with the von Neumann entropy, then solve the regularized problem using dual gradient ascent with respect to a problem-adapted norm. In particular, we show that the dual gradient norm converges to zero at a rate independent of the ambient dimension and, via rounding arguments, construct primal-feasible solutions i…

Automatic Generation of Explicit Quadratic Programming Solvers
Maximilian Schaller, Daniel Arnstr\"om, Alberto Bemporad, Stephen Boyd
https://arxiv.org/abs/2506.11513

Automatic Generation of Explicit Quadratic Programming Solvers
We consider a family of convex quadratic programs in which the coefficients of the linear objective term and the righthand side of the constraints are affine functions of a parameter. It is well known that the solution of such a parametrized quadratic program is a piecewise affine function of the parameter. The number of (polyhedral) regions in the solution map can grow exponentially in problem size, but when the number of regions is moderate, a so-called explicit solver is practical. Such a so…

An Efficient Augmented Lagrangian Method for Dynamic Optimal Transport on Surfaces Based on Second-Order Cone Programming
Liang Chen, Youyicun Lin, Yuxuan Zhou
https://arxiv.org/abs/2506.08988

An Efficient Augmented Lagrangian Method for Dynamic Optimal Transport on Surfaces Based on Second-Order Cone Programming
This paper proposes an efficient numerical optimization approach for solving dynamic optimal transport (DOT) problems on general smooth surfaces, computing both the quadratic Wasserstein distance and the associated transportation path. Building on the convex DOT model of Benamou and Brenier, we first properly reformulate its dual problem, discretized on a triangular mesh for space together with a staggered grid for time, to a linear second-order cone programming. Then the resulting finite-dimen…

Relationship between Maximum Principle and Dynamic Programming Principle for Risk-Sensitive Stochastic Optimal Control Problems with Applications
Huanqing Dong, Jingtao Shi
https://arxiv.org/abs/2507.06504

Relationship between Maximum Principle and Dynamic Programming Principle for Risk-Sensitive Stochastic Optimal Control Problems with Applications
This paper is concerned with the relationship between maximum principle and dynamic programming principle for risk-sensitive stochastic optimal control problems. Under the smooth assumption of the value function, relations among the adjoint processes, the generalized Hamiltonian function, and the value function are given. As an application, a linear-quadratic risk-sensitive portfolio optimization problem in the financial market is discussed.

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…

A Hierarchical Integer Linear Programming Approach for Optimizing Team Formation in Education
Aaron Kessler, Tim Scheiber, Heinz Schmitz, Ioanna Lykourentzou
https://arxiv.org/abs/2506.02756

A Hierarchical Integer Linear Programming Approach for Optimizing Team Formation in Education
Teamwork is integral to higher education, fostering students' interpersonal skills, improving learning outcomes, and preparing them for professional collaboration later in their careers. While team formation has traditionally been managed by humans, either instructors or students, algorithmic approaches have recently emerged to optimize this process. However, existing algorithmic team formation methods often focus on expert teams, overlook agency in choosing one's teammates, and are limited to …

Partially-Supervised Neural Network Model For Quadratic Multiparametric Programming
Fuat Can Beylunioglu, Mehrdad Pirnia, P. Robert Duimering
https://arxiv.org/abs/2506.05567

Partially-Supervised Neural Network Model For Quadratic Multiparametric Programming
Neural Networks (NN) with ReLU activation functions are used to model multiparametric quadratic optimization problems (mp-QP) in diverse engineering applications. Researchers have suggested leveraging the piecewise affine property of deep NN models to solve mp-QP with linear constraints, which also exhibit piecewise affine behaviour. However, traditional deep NN applications to mp-QP fall short of providing optimal and feasible predictions, even when trained on large datasets. This study propos…

The L-Shaped Method for Stochastic Programs with Decision-Dependent Uncertainty
Giovanni Pantuso, Mike Hewitt
https://arxiv.org/abs/2506.12753 https://

The L-Shaped Method for Stochastic Programs with Decision-Dependent Uncertainty
In this paper we extend the well-known L-Shaped method to solve two-stage stochastic programming problems with decision-dependent uncertainty. The method is based on a novel, unifying, formulation and on distribution-specific optimality and feasibility cuts for both linear and integer stochastic programs. Extensive tests on three production planning problems illustrate that the method is extremely effective on large-scale instances.

Relaxations of KKT Conditions do not Strengthen Finite RLT and SDP-RLT Bounds for Nonconvex Quadratic Programs
E. Alper Yildirim
https://arxiv.org/abs/2506.09892

Relaxations of KKT Conditions do not Strengthen Finite RLT and SDP-RLT Bounds for Nonconvex Quadratic Programs
We consider linear and semidefinite programming relaxations of nonconvex quadratic programs given by the reformulation-linearization technique (RLT relaxation), and the Shor relaxation combined with the RLT relaxation (SDP-RLT relaxation). By incorporating the first-order optimality conditions, a quadratic program can be formulated as an optimization problem with complementarity constraints. We investigate the effect of incorporating optimality conditions on the strength of the RLT and SDP-RLT …

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…

This https://arxiv.org/abs/2502.21249 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

A relax-fix-and-exclude algorithm for an MINLP problem with multilinear interpolations
This paper introduces a novel algorithm for Mixed-Integer Nonlinear Programming (MINLP) problems with multilinear interpolations of look-up tables. These problems arise when objective or constraints contain black-box functions only known at a finite set of evaluations on a predefined grid. We derive a piecewise-linear relaxation for the multilinear constraints resulting from the multilinear interpolations used to approximate the true functions. Supported by the fact that our proposed relaxation…

Optimized projection-free algorithms for online learning: construction and worst-case analysis
Julien Weibel (SIERRA), Pierre Gaillard (Thoth), Wouter M. Koolen (CWI), Adrien Taylor (SIERRA)
https://arxiv.org/abs/2506.05855

Optimized projection-free algorithms for online learning: construction and worst-case analysis
This work studies and develop projection-free algorithms for online learning with linear optimization oracles (a.k.a. Frank-Wolfe) for handling the constraint set. More precisely, this work (i) provides an improved (optimized) variant of an online Frank-Wolfe algorithm along with its conceptually simple potential-based proof, and (ii) shows how to leverage semidefinite programming to jointly design and analyze online Frank-Wolfe-type algorithms numerically in a variety of settings-that include …

GPU accelerated variant of Schroeppel-Shamir's algorithm for solving the market split problem
Nils-Christian Kempke, Thorsten Koch
https://arxiv.org/abs/2507.05045

GPU accelerated variant of Schroeppel-Shamir's algorithm for solving the market split problem
The market split problem (MSP), introduced by Cornuejols and Dawande (1998), is a challenging binary optimization problem that performs poorly on state-of-the-art linear programming-based branch-and-cut solvers. We present a novel algorithm for solving the feasibility version of this problem, derived from Schroeppel-Shamir's algorithm for the one-dimensional subset sum problem. Our approach is based on exhaustively enumerating one-dimensional solutions of MSP and utilizing GPUs to evaluate cand…

Maximal entropy in the moment body
Didier Henrion (LAAS-POP)
https://arxiv.org/abs/2507.02461 https://arxiv.org/pdf/2507.02461…

Maximal entropy in the moment body
A moment body is a linear projection of the spectraplex, the convex set of trace-one positive semidefinite matrices. Determining whether a given point lies within a given moment body is a problem with numerous applications in quantum state estimation or polynomial optimization. This moment body membership oracle can be addressed with semidefinite programming, for which several off-the-shelf interior-point solvers are available. In this paper, inspired by techniques from quantum information theo…