arXiv - MATH - Optimization and Control最新文献_第3页

Hierarchical Nash Equilibrium over Variational Equilibria via Fixed-point Set Expression of Quasi-nonexpansive Operator 通过准无展开算子的定点集合表达实现变式均衡上的分层纳什均衡

arXiv - MATH - Optimization and Control Pub Date : 2024-09-17 DOI: arxiv-2409.11094

Shota Matsuo, Keita Kume, Isao Yamada

{"title":"Hierarchical Nash Equilibrium over Variational Equilibria via Fixed-point Set Expression of Quasi-nonexpansive Operator","authors":"Shota Matsuo, Keita Kume, Isao Yamada","doi":"arxiv-2409.11094","DOIUrl":"https://doi.org/arxiv-2409.11094","url":null,"abstract":"The equilibrium selection problem in the generalized Nash equilibrium problem\u0000(GNEP) has recently been studied as an optimization problem, defined over the\u0000set of all variational equilibria achievable first through a non-cooperative\u0000game among players. However, to make such a selection fairly for all players,\u0000we have to rely on an unrealistic assumption, that is, the availability of a\u0000reliable center not possible to cause any bias for all players. In this paper,\u0000we propose a new equilibrium selection achievable by solving a further GNEP,\u0000named the hierarchical Nash equilibrium problem (HNEP), within only the\u0000players. The HNEP covers existing optimization-based equilibrium selections as\u0000its simplest cases, while the general style of the HNEP can ensure a fair\u0000equilibrium selection without assuming any trusted center or randomness. We\u0000also propose an iterative algorithm for the HNEP as an application of the\u0000hybrid steepest descent method to a variational inequality newly defined over\u0000the fixed point set of a quasi-nonexpansive operator. Numerical experiments\u0000show the effectiveness of the proposed equilibrium selection via the HNEP.","PeriodicalId":501286,"journal":{"name":"arXiv - MATH - Optimization and Control","volume":"42 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142254633","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

Inexact Riemannian Gradient Descent Method for Nonconvex Optimization 非凸优化的非精确黎曼梯度下降法

arXiv - MATH - Optimization and Control Pub Date : 2024-09-17 DOI: arxiv-2409.11181

Juan Zhou, Kangkang Deng, Hongxia Wang, Zheng Peng

{"title":"Inexact Riemannian Gradient Descent Method for Nonconvex Optimization","authors":"Juan Zhou, Kangkang Deng, Hongxia Wang, Zheng Peng","doi":"arxiv-2409.11181","DOIUrl":"https://doi.org/arxiv-2409.11181","url":null,"abstract":"Gradient descent methods are fundamental first-order optimization algorithms\u0000in both Euclidean spaces and Riemannian manifolds. However, the exact gradient\u0000is not readily available in many scenarios. This paper proposes a novel inexact\u0000Riemannian gradient descent algorithm for nonconvex problems, accompanied by a\u0000convergence guarantee. In particular, we establish two inexact gradient\u0000conditions on Riemannian manifolds for the first time, enabling precise\u0000gradient approximations. Our method demonstrates strong convergence results for\u0000both gradient sequences and function values. The global convergence with\u0000constructive convergence rates for the sequence of iterates is ensured under\u0000the Riemannian Kurdyka-L ojasiewicz property. Furthermore, our algorithm\u0000encompasses two specific applications: Riemannian sharpness-aware minimization\u0000and Riemannian extragradient algorithm, both of which inherit the global\u0000convergence properties of the inexact gradient methods. Numerical experiments\u0000on low-rank matrix completion and principal component analysis problems\u0000validate the efficiency and practical relevance of the proposed approaches.","PeriodicalId":501286,"journal":{"name":"arXiv - MATH - Optimization and Control","volume":"16 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142254612","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

A Continuous-time Tractable Model for Present-biased Agents 有现时偏见的代理的连续时间可操作模型

arXiv - MATH - Optimization and Control Pub Date : 2024-09-17 DOI: arxiv-2409.11225

Yasunori Akagi, Hideaki Kim, Takeshi Kurashima

引用次数: 0

Robust Controller Synthesis under Markovian Mode Switching with Periodic LTV Dynamics 具有周期性 LTV 动态的马尔可夫模式切换下的鲁棒控制器合成

arXiv - MATH - Optimization and Control Pub Date : 2024-09-17 DOI: arxiv-2409.11537

Shaurya Shrivastava, Kenshiro Oguri

引用次数: 0

Mixed-integer linear programming approaches for nested $p$-center problems with absolute and relative regret objectives 具有绝对和相对遗憾目标的嵌套 $p$ 中心问题的混合整数线性规划方法

arXiv - MATH - Optimization and Control Pub Date : 2024-09-17 DOI: arxiv-2409.11346

Christof Brandstetter, Markus Sinnl

{"title":"Mixed-integer linear programming approaches for nested $p$-center problems with absolute and relative regret objectives","authors":"Christof Brandstetter, Markus Sinnl","doi":"arxiv-2409.11346","DOIUrl":"https://doi.org/arxiv-2409.11346","url":null,"abstract":"We introduce the nested $p$-center problem, which is a multi-period variant\u0000of the well-known $p$-center problem. The use of the nesting concept allows to\u0000obtain solutions, which are consistent over the considered time horizon, i.e.,\u0000facilities which are opened in a given time period stay open for subsequent\u0000time periods. This is important in real-life applications, as closing (and\u0000potential later re-opening) of facilities between time periods can be\u0000undesirable. We consider two different versions of our problem, with the difference being\u0000the objective function. The first version considers the sum of the absolute\u0000regrets (of nesting) over all time periods, and the second version considers\u0000minimizing the maximum relative regret over the time periods. We present three mixed-integer programming formulations for the version with\u0000absolute regret objective and two formulations for the version with relative\u0000regret objective. For all the formulations, we present valid inequalities.\u0000Based on the formulations and the valid inequalities, we develop\u0000branch-and-bound/branch-and-cut solution algorithms. These algorithms include a\u0000preprocessing procedure that exploits the nesting property and also begins\u0000heuristics and primal heuristics. We conducted a computational study on instances from the literature for the\u0000$p$-center problem, which we adapted to our problems. We also analyse the\u0000effect of nesting on the solution cost and the number of open facilities.","PeriodicalId":501286,"journal":{"name":"arXiv - MATH - Optimization and Control","volume":"16 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142254608","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 joint eigen-decomposition of matrices 关于矩阵的联合特征分解

arXiv - MATH - Optimization and Control Pub Date : 2024-09-16 DOI: arxiv-2409.10292

Erik Troedsson, Daniel Falkowski, Carl-Fredrik Lidgren, Herwig Wendt, Marcus Carlsson

引用次数: 0

A Note on Piecewise Affine Decision Rules for Robust, Stochastic, and Data-Driven Optimization 关于用于稳健、随机和数据驱动优化的片断仿射决策规则的说明

arXiv - MATH - Optimization and Control Pub Date : 2024-09-16 DOI: arxiv-2409.10295

Simon Thomä, Maximilian Schiffer, Wolfram Wiesemann

引用次数: 0

A relative-error inexact ADMM splitting algorithm for convex optimization with inertial effects 用于具有惯性效应的凸优化的相对误差不精确 ADMM 分裂算法

arXiv - MATH - Optimization and Control Pub Date : 2024-09-16 DOI: arxiv-2409.10311

M. Marques Alves, M. Geremia

引用次数: 0

Generalization of Optimal Geodesic Curvature Constrained Dubins' Path on Sphere with Free Terminal Orientation 具有自由终端方向的球面上最优大地曲率约束杜宾斯路径的广义化

arXiv - MATH - Optimization and Control Pub Date : 2024-09-16 DOI: arxiv-2409.09954

Deepak Prakash Kumar, Swaroop Darbha, Satyanarayana Gupta Manyam, David Casbeer

{"title":"Generalization of Optimal Geodesic Curvature Constrained Dubins' Path on Sphere with Free Terminal Orientation","authors":"Deepak Prakash Kumar, Swaroop Darbha, Satyanarayana Gupta Manyam, David Casbeer","doi":"arxiv-2409.09954","DOIUrl":"https://doi.org/arxiv-2409.09954","url":null,"abstract":"In this paper, motion planning for a Dubins vehicle on a unit sphere to\u0000attain a desired final location is considered. The radius of the Dubins path on\u0000the sphere is lower bounded by $r$. In a previous study, this problem was\u0000addressed, wherein it was shown that the optimal path is of type $CG, CC,$ or a\u0000degenerate path of the same for $r leq frac{1}{2}.$ Here, $C = L, R$ denotes\u0000an arc of a tight left or right turn of minimum turning radius $r,$ and $G$\u0000denotes an arc of a great circle. In this study, the candidate paths for the\u0000same problem are generalized to model vehicles with a larger turning radius. In\u0000particular, it is shown that the candidate optimal paths are of type $CG, CC,$\u0000or a degenerate path of the same for $r leq frac{sqrt{3}}{2}.$ Noting that\u0000at most two $LG$ paths and two $RG$ paths can exist for a given final location,\u0000this article further reduces the candidate optimal paths by showing that only\u0000one $LG$ and one $RG$ path can be optimal, yielding a total of seven candidate\u0000paths for $r leq frac{sqrt{3}}{2}.$ Additional conditions for the optimality\u0000of $CC$ paths are also derived in this study.","PeriodicalId":501286,"journal":{"name":"arXiv - MATH - Optimization and Control","volume":"28 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142254538","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 Geodesic Curvature Constrained Dubins' Path on Sphere with Free Terminal Orientation 具有自由终点方向的球面上最优大地曲率约束杜宾斯路径

arXiv - MATH - Optimization and Control Pub Date : 2024-09-16 DOI: arxiv-2409.10363

Deepak Prakash Kumar, Swaroop Darbha, Satyanarayana Gupta Manyam, Dzung Tran, David W. Casbeer

引用次数: 0