Mathematical Programming最新文献_第4页

Generalized scaling for the constrained maximum-entropy sampling problem 受限最大熵抽样问题的广义缩放

IF 2.7 2区数学

Mathematical Programming Pub Date : 2024-06-20 DOI: 10.1007/s10107-024-02101-3

Zhongzhu Chen, Marcia Fampa, Jon Lee

引用次数: 0

A PTAS for the horizontal rectangle stabbing problem 水平矩形刺入问题的 PTAS

IF 2.7 2区数学

Mathematical Programming Pub Date : 2024-06-13 DOI: 10.1007/s10107-024-02106-y

Arindam Khan, Aditya Subramanian, Andreas Wiese

{"title":"A PTAS for the horizontal rectangle stabbing problem","authors":"Arindam Khan, Aditya Subramanian, Andreas Wiese","doi":"10.1007/s10107-024-02106-y","DOIUrl":"https://doi.org/10.1007/s10107-024-02106-y","url":null,"abstract":"We study rectangle stabbing problems in which we are given n axis-aligned rectangles in the plane that we want to stab, that is, we want to select line segments such that for each given rectangle there is a line segment that intersects two opposite edges of it. In the horizontal rectangle stabbing problem (Stabbing), the goal is to find a set of horizontal line segments of minimum total length such that all rectangles are stabbed. In the horizontal–vertical stabbing problem (HV-Stabbing), the goal is to find a set of rectilinear (that is, either vertical or horizontal) line segments of minimum total length such that all rectangles are stabbed. Both variants are NP-hard. Chan et al. (ISAAC, 2018) initiated the study of these problems by providing constant approximation algorithms. Recently, Eisenbrand et al. (A QPTAS for stabbing rectangles, 2021) have presented a QPTAS and a polynomial-time 8-approximation algorithm for Stabbing, but it was open whether the problem admits a PTAS. In this paper, we obtain a PTAS for Stabbing, settling this question. For HV-Stabbing, we obtain a ((2+varepsilon ))-approximation. We also obtain PTASs for special cases of HV-Stabbing: (i) when all rectangles are squares, (ii) when each rectangle’s width is at most its height, and (iii) when all rectangles are (delta )-large, that is, have at least one edge whose length is at least (delta ), while all edge lengths are at most 1. Our result also implies improved approximations for other problems such as generalized minimum Manhattan network.","PeriodicalId":18297,"journal":{"name":"Mathematical Programming","volume":"46 1","pages":""},"PeriodicalIF":2.7,"publicationDate":"2024-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141503476","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

An asynchronous proximal bundle method 异步近端捆绑法

IF 2.7 2区数学

Mathematical Programming Pub Date : 2024-06-04 DOI: 10.1007/s10107-024-02088-x

Frank Fischer

引用次数: 0

A unified framework for symmetry handling 处理对称性的统一框架

IF 2.7 2区数学

Mathematical Programming Pub Date : 2024-06-04 DOI: 10.1007/s10107-024-02102-2

Jasper van Doornmalen, Christopher Hojny

引用次数: 0

Universal heavy-ball method for nonconvex optimization under Hölder continuous Hessians 赫尔德连续赫西亚条件下非凸优化的通用重球法

IF 2.7 2区数学

Mathematical Programming Pub Date : 2024-06-04 DOI: 10.1007/s10107-024-02100-4

Naoki Marumo, Akiko Takeda

{"title":"Universal heavy-ball method for nonconvex optimization under Hölder continuous Hessians","authors":"Naoki Marumo, Akiko Takeda","doi":"10.1007/s10107-024-02100-4","DOIUrl":"https://doi.org/10.1007/s10107-024-02100-4","url":null,"abstract":"We propose a new first-order method for minimizing nonconvex functions with Lipschitz continuous gradients and Hölder continuous Hessians. The proposed algorithm is a heavy-ball method equipped with two particular restart mechanisms. It finds a solution where the gradient norm is less than (varepsilon ) in (O(H_{nu }^{frac{1}{2 + 2 nu }} varepsilon ^{- frac{4 + 3 nu }{2 + 2 nu }})) function and gradient evaluations, where (nu in [0, 1]) and (H_{nu }) are the Hölder exponent and constant, respectively. This complexity result covers the classical bound of (O(varepsilon ^{-2})) for (nu = 0) and the state-of-the-art bound of (O(varepsilon ^{-7/4})) for (nu = 1). Our algorithm is (nu )-independent and thus universal; it automatically achieves the above complexity bound with the optimal (nu in [0, 1]) without knowledge of (H_{nu }). In addition, the algorithm does not require other problem-dependent parameters as input, including the gradient’s Lipschitz constant or the target accuracy (varepsilon ). Numerical results illustrate that the proposed method is promising.","PeriodicalId":18297,"journal":{"name":"Mathematical Programming","volume":"51 1","pages":""},"PeriodicalIF":2.7,"publicationDate":"2024-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141251840","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

The complexity of first-order optimization methods from a metric perspective 从度量角度看一阶优化方法的复杂性

IF 2.7 2区数学

Mathematical Programming Pub Date : 2024-06-04 DOI: 10.1007/s10107-024-02091-2

A. S. Lewis, Tonghua Tian

引用次数: 0

Polarized consensus-based dynamics for optimization and sampling 基于共识的极化动态优化和抽样

IF 2.7 2区数学

Mathematical Programming Pub Date : 2024-05-31 DOI: 10.1007/s10107-024-02095-y

Leon Bungert, Tim Roith, Philipp Wacker

{"title":"Polarized consensus-based dynamics for optimization and sampling","authors":"Leon Bungert, Tim Roith, Philipp Wacker","doi":"10.1007/s10107-024-02095-y","DOIUrl":"https://doi.org/10.1007/s10107-024-02095-y","url":null,"abstract":"In this paper we propose polarized consensus-based dynamics in order to make consensus-based optimization (CBO) and sampling (CBS) applicable for objective functions with several global minima or distributions with many modes, respectively. For this, we “polarize” the dynamics with a localizing kernel and the resulting model can be viewed as a bounded confidence model for opinion formation in the presence of common objective. Instead of being attracted to a common weighted mean as in the original consensus-based methods, which prevents the detection of more than one minimum or mode, in our method every particle is attracted to a weighted mean which gives more weight to nearby particles. We prove that in the mean-field regime the polarized CBS dynamics are unbiased for Gaussian targets. We also prove that in the zero temperature limit and for sufficiently well-behaved strongly convex objectives the solution of the Fokker–Planck equation converges in the Wasserstein-2 distance to a Dirac measure at the minimizer. Finally, we propose a computationally more efficient generalization which works with a predefined number of clusters and improves upon our polarized baseline method for high-dimensional optimization.\u0000","PeriodicalId":18297,"journal":{"name":"Mathematical Programming","volume":"239 1","pages":""},"PeriodicalIF":2.7,"publicationDate":"2024-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141189696","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Exploiting the polyhedral geometry of stochastic linear bilevel programming 利用随机线性双层程序设计的多面体几何学

IF 2.7 2区数学

Mathematical Programming Pub Date : 2024-05-27 DOI: 10.1007/s10107-024-02097-w

Gonzalo Muñoz, David Salas, Anton Svensson

{"title":"Exploiting the polyhedral geometry of stochastic linear bilevel programming","authors":"Gonzalo Muñoz, David Salas, Anton Svensson","doi":"10.1007/s10107-024-02097-w","DOIUrl":"https://doi.org/10.1007/s10107-024-02097-w","url":null,"abstract":"We study linear bilevel programming problems whose lower-level objective is given by a random cost vector with known distribution. We consider the case where this distribution is nonatomic, allowing to reformulate the problem of the leader using the Bayesian approach in the sense of Salas and Svensson (SIAM J Optim 33(3):2311–2340, 2023), with a decision-dependent distribution that concentrates on the vertices of the feasible set of the follower’s problem. We call this a vertex-supported belief. We prove that this formulation is piecewise affine over the so-called chamber complex of the feasible set of the high-point relaxation. We propose two algorithmic approaches to solve general problems enjoying this last property. The first one is based on enumerating the vertices of the chamber complex. This approach is not scalable, but we present it as a computational baseline and for its theoretical interest. The second one is a Monte-Carlo approximation scheme based on the fact that randomly drawn points of the domain lie, with probability 1, in the interior of full-dimensional chambers, where the problem (restricted to this chamber) can be reduced to a linear program. Finally, we evaluate these methods through computational experiments showing both approaches’ advantages and challenges.\u0000","PeriodicalId":18297,"journal":{"name":"Mathematical Programming","volume":"70 1","pages":""},"PeriodicalIF":2.7,"publicationDate":"2024-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141171635","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

ReLU neural networks of polynomial size for exact maximum flow computation 用于精确最大流量计算的多项式大小 ReLU 神经网络

IF 2.7 2区数学

Mathematical Programming Pub Date : 2024-05-25 DOI: 10.1007/s10107-024-02096-x

Christoph Hertrich, Leon Sering

引用次数: 0

A tight $$(1.5+epsilon )$$ -approximation for unsplittable capacitated vehicle routing on trees 树上不可分容车辆路由的$$(1.5+epsilon )$$ 精确近似值

IF 2.7 2区数学

Mathematical Programming Pub Date : 2024-05-25 DOI: 10.1007/s10107-024-02094-z

Claire Mathieu, Hang Zhou

{"title":"A tight $$(1.5+epsilon )$$ -approximation for unsplittable capacitated vehicle routing on trees","authors":"Claire Mathieu, Hang Zhou","doi":"10.1007/s10107-024-02094-z","DOIUrl":"https://doi.org/10.1007/s10107-024-02094-z","url":null,"abstract":"In the unsplittable capacitated vehicle routing problem (UCVRP) on trees, we are given a rooted tree with edge weights and a subset of vertices of the tree called terminals. Each terminal is associated with a positive demand between 0 and 1. The goal is to find a minimum length collection of tours starting and ending at the root of the tree such that the demand of each terminal is covered by a single tour (i.e., the demand cannot be split), and the total demand of the terminals in each tour does not exceed the capacity of 1.For the special case when all terminals have equal demands, a long line of research culminated in a quasi-polynomial time approximation scheme [Jayaprakash and Salavatipour, TALG 2023] and a polynomial time approximation scheme [Mathieu and Zhou, TALG 2023].In this work, we study the general case when the terminals have arbitrary demands. Our main contribution is a polynomial time ((1.5+epsilon ))-approximation algorithm for the UCVRP on trees. This is the first improvement upon the 2-approximation algorithm more than 30 years ago. Our approximation ratio is essentially best possible, since it is NP-hard to approximate the UCVRP on trees to better than a 1.5 factor.","PeriodicalId":18297,"journal":{"name":"Mathematical Programming","volume":"75 1","pages":""},"PeriodicalIF":2.7,"publicationDate":"2024-05-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141153885","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0