arXiv - MATH - Optimization and Control最新文献_第7页

Markovian Foundations for Quasi-Stochastic Approximation in Two Timescales: Extended Version 双时标准随机逼近的马尔可夫基础扩展版

arXiv - MATH - Optimization and Control Pub Date : 2024-09-12 DOI: arxiv-2409.07842

Caio Kalil Lauand, Sean Meyn

引用次数: 0

Learning incomplete factorization preconditioners for GMRES 为 GMRES 学习不完全因式分解预处理器

arXiv - MATH - Optimization and Control Pub Date : 2024-09-12 DOI: arxiv-2409.08262

Paul Häusner, Aleix Nieto Juscafresa, Jens Sjölund

{"title":"Learning incomplete factorization preconditioners for GMRES","authors":"Paul Häusner, Aleix Nieto Juscafresa, Jens Sjölund","doi":"arxiv-2409.08262","DOIUrl":"https://doi.org/arxiv-2409.08262","url":null,"abstract":"In this paper, we develop a data-driven approach to generate incomplete LU\u0000factorizations of large-scale sparse matrices. The learned approximate\u0000factorization is utilized as a preconditioner for the corresponding linear\u0000equation system in the GMRES method. Incomplete factorization methods are one\u0000of the most commonly applied algebraic preconditioners for sparse linear\u0000equation systems and are able to speed up the convergence of Krylov subspace\u0000methods. However, they are sensitive to hyper-parameters and might suffer from\u0000numerical breakdown or lead to slow convergence when not properly applied. We\u0000replace the typically hand-engineered algorithms with a graph neural network\u0000based approach that is trained against data to predict an approximate\u0000factorization. This allows us to learn preconditioners tailored for a specific\u0000problem distribution. We analyze and empirically evaluate different loss\u0000functions to train the learned preconditioners and show their effectiveness to\u0000decrease the number of GMRES iterations and improve the spectral properties on\u0000our synthetic dataset. The code is available at\u0000https://github.com/paulhausner/neural-incomplete-factorization.","PeriodicalId":501286,"journal":{"name":"arXiv - MATH - Optimization and Control","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142212371","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Self-Supervised Learning of Iterative Solvers for Constrained Optimization 约束优化迭代求解器的自监督学习

arXiv - MATH - Optimization and Control Pub Date : 2024-09-12 DOI: arxiv-2409.08066

Lukas Lüken, Sergio Lucia

{"title":"Self-Supervised Learning of Iterative Solvers for Constrained Optimization","authors":"Lukas Lüken, Sergio Lucia","doi":"arxiv-2409.08066","DOIUrl":"https://doi.org/arxiv-2409.08066","url":null,"abstract":"Obtaining the solution of constrained optimization problems as a function of\u0000parameters is very important in a multitude of applications, such as control\u0000and planning. Solving such parametric optimization problems in real time can\u0000present significant challenges, particularly when it is necessary to obtain\u0000highly accurate solutions or batches of solutions. To solve these challenges,\u0000we propose a learning-based iterative solver for constrained optimization which\u0000can obtain very fast and accurate solutions by customizing the solver to a\u0000specific parametric optimization problem. For a given set of parameters of the\u0000constrained optimization problem, we propose a first step with a neural network\u0000predictor that outputs primal-dual solutions of a reasonable degree of\u0000accuracy. This primal-dual solution is then improved to a very high degree of\u0000accuracy in a second step by a learned iterative solver in the form of a neural\u0000network. A novel loss function based on the Karush-Kuhn-Tucker conditions of\u0000optimality is introduced, enabling fully self-supervised training of both\u0000neural networks without the necessity of prior sampling of optimizer solutions.\u0000The evaluation of a variety of quadratic and nonlinear parametric test problems\u0000demonstrates that the predictor alone is already competitive with recent\u0000self-supervised schemes for approximating optimal solutions. The second step of\u0000our proposed learning-based iterative constrained optimizer achieves solutions\u0000with orders of magnitude better accuracy than other learning-based approaches,\u0000while being faster to evaluate than state-of-the-art solvers and natively\u0000allowing for GPU parallelization.","PeriodicalId":501286,"journal":{"name":"arXiv - MATH - Optimization and Control","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142212372","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Multi-period railway line planning for integrated passenger-freight transportation 客货运输一体化的多期铁路线路规划

arXiv - MATH - Optimization and Control Pub Date : 2024-09-12 DOI: arxiv-2409.08256

Wanru Chen, Rolf N. van Lieshout, Dezhi Zhang, Tom Van Woensel

{"title":"Multi-period railway line planning for integrated passenger-freight transportation","authors":"Wanru Chen, Rolf N. van Lieshout, Dezhi Zhang, Tom Van Woensel","doi":"arxiv-2409.08256","DOIUrl":"https://doi.org/arxiv-2409.08256","url":null,"abstract":"This paper addresses a multi-period line planning problem in an integrated\u0000passenger-freight railway system, aiming to maximize profit while serving\u0000passengers and freight using a combination of dedicated passenger trains,\u0000dedicated freight trains, and mixed trains. To accommodate demand with\u0000different time sensitivities, we develop a period-extended change&go-network\u0000that tracks the paths taken by passengers and freight. The problem is\u0000formulated as a path-based mixed integer programming model, with the linear\u0000relaxation solved using column generation. Paths for passengers and freight are\u0000dynamically generated by solving pricing problems defined as elementary\u0000shortest-path problems with duration constraints. We propose two heuristic\u0000approaches: price-and-branch and a diving heuristic, with acceleration\u0000strategies, to find integer feasible solutions efficiently. Computational\u0000experiments on the Chinese high-speed railway network demonstrate that the\u0000diving heuristic outperforms the price-and-branch heuristic in both\u0000computational time and solution quality. Additionally, the experiments\u0000highlight the benefits of integrating freight, the advantages of multi-period\u0000line planning, and the impact of different demand patterns on line operations.","PeriodicalId":501286,"journal":{"name":"arXiv - MATH - Optimization and Control","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142212361","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Optimal Consumption for Recursive Preferences with Local Substitution under Risk 风险条件下具有局部替代性的递归偏好的最优消费

arXiv - MATH - Optimization and Control Pub Date : 2024-09-12 DOI: arxiv-2409.07799

Hanwu Li, Frank Riedel

引用次数: 0

How can the tragedy of the commons be prevented?: Introducing Linear Quadratic Mixed Mean Field Games 如何防止公地悲剧？线性二次混合均值场博弈介绍

arXiv - MATH - Optimization and Control Pub Date : 2024-09-12 DOI: arxiv-2409.08235

Gokce Dayanikli, Mathieu Lauriere

{"title":"How can the tragedy of the commons be prevented?: Introducing Linear Quadratic Mixed Mean Field Games","authors":"Gokce Dayanikli, Mathieu Lauriere","doi":"arxiv-2409.08235","DOIUrl":"https://doi.org/arxiv-2409.08235","url":null,"abstract":"In a regular mean field game (MFG), the agents are assumed to be\u0000insignificant, they do not realize their effect on the population level and\u0000this may result in a phenomenon coined as the Tragedy of the Commons by the\u0000economists. However, in real life this phenomenon is often avoided thanks to\u0000the underlying altruistic behavior of (all or some of the) agents. Motivated by\u0000this observation, we introduce and analyze two different mean field models to\u0000include altruism in the decision making of agents. In the first model, mixed\u0000individual MFGs, there are infinitely many agents who are partially altruistic\u0000(i.e., they behave partially cooperatively) and partially non-cooperative. In\u0000the second model, mixed population MFGs, one part of the population behaves\u0000cooperatively and the remaining agents behave non-cooperatively. Both models\u0000are introduced in a general linear quadratic framework for which we\u0000characterize the equilibrium via forward backward stochastic differential\u0000equations. Furthermore, we give explicit solutions in terms of ordinary\u0000differential equations, and prove the existence and uniqueness results.","PeriodicalId":501286,"journal":{"name":"arXiv - MATH - Optimization and Control","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142212362","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Duality theory in linear optimization and its extensions -- formally verified 线性优化及其扩展中的对偶理论 -- 正式验证

arXiv - MATH - Optimization and Control Pub Date : 2024-09-12 DOI: arxiv-2409.08119

Martin Dvorak, Vladimir Kolmogorov

引用次数: 0

Accelerated Multi-Time-Scale Stochastic Approximation: Optimal Complexity and Applications in Reinforcement Learning and Multi-Agent Games 加速多时间尺度随机逼近：最优复杂性及其在强化学习和多代理游戏中的应用

arXiv - MATH - Optimization and Control Pub Date : 2024-09-12 DOI: arxiv-2409.07767

Sihan Zeng, Thinh T. Doan

{"title":"Accelerated Multi-Time-Scale Stochastic Approximation: Optimal Complexity and Applications in Reinforcement Learning and Multi-Agent Games","authors":"Sihan Zeng, Thinh T. Doan","doi":"arxiv-2409.07767","DOIUrl":"https://doi.org/arxiv-2409.07767","url":null,"abstract":"Multi-time-scale stochastic approximation is an iterative algorithm for\u0000finding the fixed point of a set of $N$ coupled operators given their noisy\u0000samples. It has been observed that due to the coupling between the decision\u0000variables and noisy samples of the operators, the performance of this method\u0000decays as $N$ increases. In this work, we develop a new accelerated variant of\u0000multi-time-scale stochastic approximation, which significantly improves the\u0000convergence rates of its standard counterpart. Our key idea is to introduce\u0000auxiliary variables to dynamically estimate the operators from their samples,\u0000which are then used to update the decision variables. These auxiliary variables\u0000help not only to control the variance of the operator estimates but also to\u0000decouple the sampling noise and the decision variables. This allows us to\u0000select more aggressive step sizes to achieve an optimal convergence rate.\u0000Specifically, under a strong monotonicity condition, we show that for any value\u0000of $N$ the $t^{text{th}}$ iterate of the proposed algorithm converges to the\u0000desired solution at a rate $widetilde{O}(1/t)$ when the operator samples are\u0000generated from a single from Markov process trajectory. A second contribution of this work is to demonstrate that the objective of a\u0000range of problems in reinforcement learning and multi-agent games can be\u0000expressed as a system of fixed-point equations. As such, the proposed approach\u0000can be used to design new learning algorithms for solving these problems. We\u0000illustrate this observation with numerical simulations in a multi-agent game\u0000and show the advantage of the proposed method over the standard\u0000multi-time-scale stochastic approximation algorithm.","PeriodicalId":501286,"journal":{"name":"arXiv - MATH - Optimization and Control","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142212368","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

On an optimization model for firefighting helicopter planning 关于消防直升机规划的优化模型

arXiv - MATH - Optimization and Control Pub Date : 2024-09-12 DOI: arxiv-2409.07937

Marta Rodríguez Barreiro, María José Ginzo Villamayor, Fernando Pérez Porras, María Luisa Carpente Rodríguez, Silvia María Lorenzo Freire

{"title":"On an optimization model for firefighting helicopter planning","authors":"Marta Rodríguez Barreiro, María José Ginzo Villamayor, Fernando Pérez Porras, María Luisa Carpente Rodríguez, Silvia María Lorenzo Freire","doi":"arxiv-2409.07937","DOIUrl":"https://doi.org/arxiv-2409.07937","url":null,"abstract":"During a wildfire, the work of the aerial coordinator is crucial for the\u0000control of the wildfire and the minimization of the burned area and the damage\u0000caused. Since it could be very useful for the coordinator to have\u0000decision-making tools at his/her disposal, this framework deals with an\u0000optimization model to obtain the optimal planning of firefighting helicopters,\u0000deciding the points where the aircraft should load water, the areas of the\u0000wildfire where they should work, and the rest bases to which each helicopter\u0000should be assigned. It was developed a Mixed Integer Linear Programming model\u0000which takes into account the configuration of helicopters, in closed circuits,\u0000as well as the flight aerial regulations in Spain. Due to the complexity of the\u0000model, two algorithms are developed, based on the Simulated Annealing and\u0000Iterated Local Search metaheuristic techniques. Both algorithms are tested with\u0000real data instances, obtaining very promising results for future application in\u0000the planning of aircraft throughout a wildfire evolution.","PeriodicalId":501286,"journal":{"name":"arXiv - MATH - Optimization and Control","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142212365","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Optimal control for coupled sweeping processes under minimal assumptions 最小假设条件下耦合扫频过程的最优控制

arXiv - MATH - Optimization and Control Pub Date : 2024-09-12 DOI: arxiv-2409.07722

Samara Chamoun, Vera Zeidan

引用次数: 0