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Fast algorithms for maximizing the minimum eigenvalue in fixed dimension 固定维度下最小特征值最大化的快速算法
IF 0.8 4区 管理学
Operations Research Letters Pub Date : 2024-09-13 DOI: 10.1016/j.orl.2024.107186
Adam Brown , Aditi Laddha , Mohit Singh
{"title":"Fast algorithms for maximizing the minimum eigenvalue in fixed dimension","authors":"Adam Brown ,&nbsp;Aditi Laddha ,&nbsp;Mohit Singh","doi":"10.1016/j.orl.2024.107186","DOIUrl":"10.1016/j.orl.2024.107186","url":null,"abstract":"<div><div>In the minimum eigenvalue problem, we are given a collection of vectors in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup></math></span>, and the goal is to pick a subset <em>B</em> to maximize the minimum eigenvalue of the matrix <span><math><msub><mrow><mo>∑</mo></mrow><mrow><mi>i</mi><mo>∈</mo><mi>B</mi></mrow></msub><msub><mrow><mi>v</mi></mrow><mrow><mi>i</mi></mrow></msub><msubsup><mrow><mi>v</mi></mrow><mrow><mi>i</mi></mrow><mrow><mo>⊤</mo></mrow></msubsup></math></span>. We give a <span><math><mi>O</mi><mrow><mo>(</mo><msup><mrow><mi>n</mi></mrow><mrow><mi>O</mi><mo>(</mo><mi>d</mi><mi>log</mi><mo>⁡</mo><mo>(</mo><mi>d</mi><mo>)</mo><mo>/</mo><msup><mrow><mi>ϵ</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></mrow></msup><mo>)</mo></mrow></math></span>-time randomized algorithm that finds an assignment subject to a partition constraint whose minimum eigenvalue is at least <span><math><mo>(</mo><mn>1</mn><mo>−</mo><mi>ϵ</mi><mo>)</mo></math></span> times the optimum, with high probability. As a byproduct, we also get a simple algorithm for an algorithmic version of Kadison-Singer problem.</div></div>","PeriodicalId":54682,"journal":{"name":"Operations Research Letters","volume":"57 ","pages":"Article 107186"},"PeriodicalIF":0.8,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142310535","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On the nature of Bregman functions 关于布雷格曼函数的性质
IF 0.8 4区 管理学
Operations Research Letters Pub Date : 2024-09-12 DOI: 10.1016/j.orl.2024.107183
Edouard Pauwels
{"title":"On the nature of Bregman functions","authors":"Edouard Pauwels","doi":"10.1016/j.orl.2024.107183","DOIUrl":"10.1016/j.orl.2024.107183","url":null,"abstract":"<div><p>Let <span><math><mi>C</mi><mo>⊂</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span> be convex, compact, with nonempty interior and <em>h</em> be Legendre with domain <em>C</em>, continuous on <em>C</em>. We prove that <em>h</em> is Bregman if and only if it is strictly convex on <em>C</em> and <em>C</em> is a polytope. This provides insights on sequential convergence of many Bregman divergence based algorithm: abstract compatibility conditions between Bregman and Euclidean topology may equivalently be replaced by explicit conditions on <em>h</em> and <em>C</em>. This also emphasizes that a general convergence theory for these methods (beyond polyhedral domains) would require more refinements than Bregman's conditions.</p></div>","PeriodicalId":54682,"journal":{"name":"Operations Research Letters","volume":"57 ","pages":"Article 107183"},"PeriodicalIF":0.8,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0167637724001196/pdfft?md5=0177e635704d60cd488a1b496a65610b&pid=1-s2.0-S0167637724001196-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142173344","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Efficient sampling from phase-type distributions 从相位型分布中高效采样
IF 0.8 4区 管理学
Operations Research Letters Pub Date : 2024-09-10 DOI: 10.1016/j.orl.2024.107184
Dieter Fiems
{"title":"Efficient sampling from phase-type distributions","authors":"Dieter Fiems","doi":"10.1016/j.orl.2024.107184","DOIUrl":"10.1016/j.orl.2024.107184","url":null,"abstract":"<div><p>A phase-type distributed random variable represents the time to absorption of a Markov chain with an absorbing state. In this letter, we show that the alias method can be modified to efficiently generate phase-type distributed random variables. Both initialisation and generation are fast, at the cost of larger memory requirements. Numerical experiments show that the proposed method significantly reduces the computation time compared to direct simulation.</p></div>","PeriodicalId":54682,"journal":{"name":"Operations Research Letters","volume":"57 ","pages":"Article 107184"},"PeriodicalIF":0.8,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142162185","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A bargaining game for implementing the equal gain splitting rule in sequencing situations 在排序情况下实施等额收益分割规则的讨价还价游戏
IF 0.8 4区 管理学
Operations Research Letters Pub Date : 2024-09-05 DOI: 10.1016/j.orl.2024.107182
Guangjing Yang
{"title":"A bargaining game for implementing the equal gain splitting rule in sequencing situations","authors":"Guangjing Yang","doi":"10.1016/j.orl.2024.107182","DOIUrl":"10.1016/j.orl.2024.107182","url":null,"abstract":"<div><p>This paper investigates non-cooperative behavior in single-machine scheduling and aims to implement the equal gain splitting (EGS) rule via a designed bargaining game. In this game, randomly chosen proposers make offers that coalition members can accept or reject, with the goal of reaching subgame perfect equilibria that align with the EGS rule. Additionally, we extend the game to implement the weighted gain splitting (WGS) rule, which is a generalization of the EGS rule considering players' weights.</p></div>","PeriodicalId":54682,"journal":{"name":"Operations Research Letters","volume":"57 ","pages":"Article 107182"},"PeriodicalIF":0.8,"publicationDate":"2024-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142149958","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A feasible smoothing accelerated projected gradient method for nonsmooth convex optimization 非光滑凸优化的可行平滑加速投影梯度法
IF 0.8 4区 管理学
Operations Research Letters Pub Date : 2024-09-02 DOI: 10.1016/j.orl.2024.107181
Akatsuki Nishioka , Yoshihiro Kanno
{"title":"A feasible smoothing accelerated projected gradient method for nonsmooth convex optimization","authors":"Akatsuki Nishioka ,&nbsp;Yoshihiro Kanno","doi":"10.1016/j.orl.2024.107181","DOIUrl":"10.1016/j.orl.2024.107181","url":null,"abstract":"<div><p>Smoothing accelerated gradient methods achieve faster convergence rates than that of the subgradient method for some nonsmooth convex optimization problems. However, Nesterov's extrapolation may require gradients at infeasible points, and thus they cannot be applied to some structural optimization problems. We introduce a variant of smoothing accelerated projected gradient methods where every variable is feasible. The <span><math><mi>O</mi><mo>(</mo><msup><mrow><mi>k</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup><mi>log</mi><mo>⁡</mo><mi>k</mi><mo>)</mo></math></span> convergence rate is obtained using the Lyapunov function. We conduct a numerical experiment on the robust compliance optimization of a truss structure.</p></div>","PeriodicalId":54682,"journal":{"name":"Operations Research Letters","volume":"57 ","pages":"Article 107181"},"PeriodicalIF":0.8,"publicationDate":"2024-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0167637724001172/pdfft?md5=461018257332522ab26dc80e977a24bc&pid=1-s2.0-S0167637724001172-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142149957","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Freight consolidation through carrier collaboration - A cooperative game 通过承运商合作实现货运整合--一场合作游戏
IF 0.8 4区 管理学
Operations Research Letters Pub Date : 2024-09-01 DOI: 10.1016/j.orl.2024.107142
Fabio Mercurio , Loe Schlicher , Sonja U.K. Rohmer , Tom Van Woensel
{"title":"Freight consolidation through carrier collaboration - A cooperative game","authors":"Fabio Mercurio ,&nbsp;Loe Schlicher ,&nbsp;Sonja U.K. Rohmer ,&nbsp;Tom Van Woensel","doi":"10.1016/j.orl.2024.107142","DOIUrl":"10.1016/j.orl.2024.107142","url":null,"abstract":"<div><p>Reducing inefficient truck movements, this research investigates the potential of freight consolidation through carrier collaboration. Considering the financial benefits of consolidation as well as the additional cost arising from collaboration, we introduce a cooperative game in which several carriers can collaborate by pooling transportation capacities. Although the core of this game can be empty, we provide three conditions under which core non-emptiness is preserved. Numerical experiments indicate, moreover, that core non-emptiness is also likely outside these conditions.</p></div>","PeriodicalId":54682,"journal":{"name":"Operations Research Letters","volume":"56 ","pages":"Article 107142"},"PeriodicalIF":0.8,"publicationDate":"2024-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0167637724000786/pdfft?md5=5809e63fd937c8a7e25f21eac97849ad&pid=1-s2.0-S0167637724000786-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141716804","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Cost allocation for set covering: The happy nucleolus 成套覆盖的成本分配：快乐的核仁
IF 0.8 4区 管理学
Operations Research Letters Pub Date : 2024-08-28 DOI: 10.1016/j.orl.2024.107158
Jannis Blauth, Antonia Ellerbrock, Vera Traub, Jens Vygen
{"title":"Cost allocation for set covering: The happy nucleolus","authors":"Jannis Blauth,&nbsp;Antonia Ellerbrock,&nbsp;Vera Traub,&nbsp;Jens Vygen","doi":"10.1016/j.orl.2024.107158","DOIUrl":"10.1016/j.orl.2024.107158","url":null,"abstract":"<div><p>We consider cost allocation for set covering problems. We allocate as much cost to the elements (players) as possible without violating the group rationality condition, and so that the excess vector is lexicographically maximized. This <em>happy nucleolus</em> has several nice properties. In particular, we show that it can be computed considering a small subset of “simple” coalitions only. While computing the nucleolus for set covering is NP-hard, our results imply that the happy nucleolus can be computed in polynomial time.</p></div>","PeriodicalId":54682,"journal":{"name":"Operations Research Letters","volume":"57 ","pages":"Article 107158"},"PeriodicalIF":0.8,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0167637724000944/pdfft?md5=454040e1a23cb747f7de28cf7ad50ee4&pid=1-s2.0-S0167637724000944-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142162184","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On a variant of the change-making problem 关于变革问题的一个变式
IF 0.8 4区 管理学
Operations Research Letters Pub Date : 2024-08-26 DOI: 10.1016/j.orl.2024.107165
Adam N. Letchford , Licong Cheng
{"title":"On a variant of the change-making problem","authors":"Adam N. Letchford ,&nbsp;Licong Cheng","doi":"10.1016/j.orl.2024.107165","DOIUrl":"10.1016/j.orl.2024.107165","url":null,"abstract":"<div><p>The <em>change-making problem</em> (CMP), introduced in 1970, is a classic problem in combinatorial optimisation. It was proven to be <em>NP</em>-hard in 1975, but it can be solved in pseudo-polynomial time by dynamic programming. In 1999, Heipcke presented a variant of the CMP which, at first glance, looks harder than the standard version. We show that, in fact, her variant can be solved in polynomial time.</p></div>","PeriodicalId":54682,"journal":{"name":"Operations Research Letters","volume":"57 ","pages":"Article 107165"},"PeriodicalIF":0.8,"publicationDate":"2024-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0167637724001019/pdfft?md5=e0e9fdd931b3a9fcee0ea8ad8811494d&pid=1-s2.0-S0167637724001019-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142096267","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Proximity guarantees of a lift-and-project approach for the cardinality-constrained Boolean quadric polytope 针对有数量限制的布尔四元多面体的举一反三法的邻近性保证
IF 0.8 4区 管理学
Operations Research Letters Pub Date : 2024-08-26 DOI: 10.1016/j.orl.2024.107166
Walid Ben-Ameur
{"title":"Proximity guarantees of a lift-and-project approach for the cardinality-constrained Boolean quadric polytope","authors":"Walid Ben-Ameur","doi":"10.1016/j.orl.2024.107166","DOIUrl":"10.1016/j.orl.2024.107166","url":null,"abstract":"<div><p>We consider a lift-and-project approach for the cardinality-constrained Boolean quadric polytope. Some upper bounds for the distance between the polytope and its linear approximation are derived. Unsurprisingly, the distance converges to 0 when the number of variables increases sufficiently.</p></div>","PeriodicalId":54682,"journal":{"name":"Operations Research Letters","volume":"57 ","pages":"Article 107166"},"PeriodicalIF":0.8,"publicationDate":"2024-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142096990","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The principle of optimality in dynamic programming: A pedagogical note 动态编程中的最优原则：教学说明
IF 0.8 4区 管理学
Operations Research Letters Pub Date : 2024-08-23 DOI: 10.1016/j.orl.2024.107164
Bar Light
{"title":"The principle of optimality in dynamic programming: A pedagogical note","authors":"Bar Light","doi":"10.1016/j.orl.2024.107164","DOIUrl":"10.1016/j.orl.2024.107164","url":null,"abstract":"<div><p>The principle of optimality is a fundamental aspect of dynamic programming, which states that the optimal solution to a dynamic optimization problem can be found by combining the optimal solutions to its sub-problems. While this principle is generally applicable, it is often only taught for problems with finite or countable state spaces in order to sidestep measure-theoretic complexities. Therefore, it cannot be applied to classic models such as inventory management and dynamic pricing models that have continuous state spaces, and students may not be aware of the possible challenges involved in studying dynamic programming models with general state spaces. To address this, we provide conditions and a self-contained simple proof that establish when the principle of optimality for discounted dynamic programming is valid. These conditions shed light on the difficulties that may arise in the general state space case. We provide examples from the literature that include the relatively involved case of universally measurable dynamic programming and the simple case of finite dynamic programming where our main result can be applied to show that the principle of optimality holds.</p></div>","PeriodicalId":54682,"journal":{"name":"Operations Research Letters","volume":"57 ","pages":"Article 107164"},"PeriodicalIF":0.8,"publicationDate":"2024-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142084097","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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