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A novel stepsize for gradient descent method 梯度下降法的新型步长
IF 1.1 4区 管理学
Operations Research Letters Pub Date : 2024-01-24 DOI: 10.1016/j.orl.2024.107072
Pham Thi Hoai , Nguyen The Vinh , Nguyen Phung Hai Chung
{"title":"A novel stepsize for gradient descent method","authors":"Pham Thi Hoai ,&nbsp;Nguyen The Vinh ,&nbsp;Nguyen Phung Hai Chung","doi":"10.1016/j.orl.2024.107072","DOIUrl":"10.1016/j.orl.2024.107072","url":null,"abstract":"<div><p>We propose a novel adaptive stepsize for the gradient descent scheme to solve unconstrained nonlinear optimization problems. With the convex and smooth objective satisfying locally Lipschitz gradient we obtain the complexity <span><math><mi>O</mi><mrow><mo>(</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mi>k</mi></mrow></mfrac><mo>)</mo></mrow></math></span> of <span><math><mi>f</mi><mo>(</mo><msup><mrow><mi>x</mi></mrow><mrow><mi>k</mi></mrow></msup><mo>)</mo><mo>−</mo><msub><mrow><mi>f</mi></mrow><mrow><mo>⁎</mo></mrow></msub></math></span><span> at most. By using the idea of the new stepsize, we propose another new algorithm based on the projected gradient for solving a class of nonconvex optimization problems over a closed convex set. The computational experiments show the efficiency of the new method.</span></p></div>","PeriodicalId":54682,"journal":{"name":"Operations Research Letters","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2024-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139578528","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
Bounds on revenue for the random consideration set choice model 随机考虑集选择模型的收入界限
IF 1.1 4区 管理学
Operations Research Letters Pub Date : 2024-01-18 DOI: 10.1016/j.orl.2024.107070
Wentao Lu
{"title":"Bounds on revenue for the random consideration set choice model","authors":"Wentao Lu","doi":"10.1016/j.orl.2024.107070","DOIUrl":"10.1016/j.orl.2024.107070","url":null,"abstract":"<div><p>The random consideration set choice model is a recently proposed choice model that can capture the stochastic choice behavior of consumers. One advantage of the random consideration set choice model is that it can accommodate some phenomena that cannot be explained by the multinomial logit model<span>. In this paper, we prove revenue bounds when the attention probabilities and preference order over products change for the random consideration set model. The bounds proposed can be used to control revenue differences when consumers' preference over product changes and can be useful for settings like online assortment optimization with a non-stationary environment.</span></p></div>","PeriodicalId":54682,"journal":{"name":"Operations Research Letters","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2024-01-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139516242","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
Max cut and semidefinite rank 最大切割和半定秩
IF 1.1 4区 管理学
Operations Research Letters Pub Date : 2024-01-17 DOI: 10.1016/j.orl.2024.107067
Renee Mirka, David P. Williamson
{"title":"Max cut and semidefinite rank","authors":"Renee Mirka,&nbsp;David P. Williamson","doi":"10.1016/j.orl.2024.107067","DOIUrl":"10.1016/j.orl.2024.107067","url":null,"abstract":"<div><p><span>This paper considers the relationship between semidefinite programs (SDPs), matrix rank, and maximum cuts of graphs. Utilizing complementary slackness conditions for SDPs, we investigate when the rank 1 feasible solution corresponding to a max cut is the unique optimal solution to the Goemans-Williamson max cut SDP by showing the existence of an optimal dual solution with rank </span><span><math><mi>n</mi><mo>−</mo><mn>1</mn></math></span><span>. Our results consider connected bipartite graphs and graphs with multiple max cuts. We conclude with a conjecture for general graphs.</span></p></div>","PeriodicalId":54682,"journal":{"name":"Operations Research Letters","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2024-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139518690","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
Demand information sharing in Cournot-Bertrand model 库诺-伯特兰模型中的需求信息共享
IF 1.1 4区 管理学
Operations Research Letters Pub Date : 2024-01-17 DOI: 10.1016/j.orl.2024.107069
Abdul Quadir
{"title":"Demand information sharing in Cournot-Bertrand model","authors":"Abdul Quadir","doi":"10.1016/j.orl.2024.107069","DOIUrl":"10.1016/j.orl.2024.107069","url":null,"abstract":"<div><p>We consider a Cournot-Bertrand competition with uncertain demand where firms receive private information about it. We prove that sharing information is a dominant strategy for the quantity-setting firm and not sharing is a dominant strategy for the price-setting firm. We uncover that the quantity-setting firm enjoys higher expected profits with more precise information and pools the information, whereas the price-setting firm's decision to pool the information depends on competition levels and a side payment. Consumers benefit from higher accuracy and pooling of information.</p></div>","PeriodicalId":54682,"journal":{"name":"Operations Research Letters","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2024-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139495165","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
Must pollution abatement harm the supplier in a multi-echelon supply chain? 在多层次供应链中，减少污染一定会损害供应商吗？
IF 1.1 4区 管理学
Operations Research Letters Pub Date : 2024-01-17 DOI: 10.1016/j.orl.2024.107066
Ismail Saglam
{"title":"Must pollution abatement harm the supplier in a multi-echelon supply chain?","authors":"Ismail Saglam","doi":"10.1016/j.orl.2024.107066","DOIUrl":"10.1016/j.orl.2024.107066","url":null,"abstract":"<div><p>This paper studies the welfare effects of the abatement cost burden of a supplier in a multi-echelon supply chain. We theoretically show that the profits of all echelons other than the supplier become lower when the supplier contributes more to the abatement. Also, we computationally show that the profit of the supplier may be higher when it makes a small amount of contribution to the abatement provided that the demand curve faced by the retailer is sufficiently linear.</p></div>","PeriodicalId":54682,"journal":{"name":"Operations Research Letters","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2024-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139509107","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 note on quadratic constraints with indicator variables: Convex hull description and perspective relaxation 关于带有指示变量的二次约束的说明：凸壳描述与透视松弛
IF 1.1 4区 管理学
Operations Research Letters Pub Date : 2024-01-01 DOI: 10.1016/j.orl.2023.107059
Andrés Gómez , Weijun Xie
{"title":"A note on quadratic constraints with indicator variables: Convex hull description and perspective relaxation","authors":"Andrés Gómez ,&nbsp;Weijun Xie","doi":"10.1016/j.orl.2023.107059","DOIUrl":"10.1016/j.orl.2023.107059","url":null,"abstract":"<div><p>In this paper, we study the mixed-integer nonlinear set given by a separable quadratic constraint<span> on continuous variables, where each continuous variable is controlled by an additional indicator. This set occurs pervasively in optimization problems with uncertainty and in machine learning. We show that optimization over this set is NP-hard. Despite this negative result, we discover links between the convex hull of the set under study, and a family of polyhedral sets studied in the literature. Moreover, we show that although perspective relaxation in the literature for this set fails to match the structure of its convex hull, it is guaranteed to be a close approximation.</span></p></div>","PeriodicalId":54682,"journal":{"name":"Operations Research Letters","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138823580","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 Gaussian Markov processes and Polya processes 论高斯马尔可夫过程和波利亚过程
IF 1.1 4区 管理学
Operations Research Letters Pub Date : 2024-01-01 DOI: 10.1016/j.orl.2023.107062
Kerry Fendick , Ward Whitt
{"title":"On Gaussian Markov processes and Polya processes","authors":"Kerry Fendick ,&nbsp;Ward Whitt","doi":"10.1016/j.orl.2023.107062","DOIUrl":"10.1016/j.orl.2023.107062","url":null,"abstract":"<div><p><span><span><span>In previous work we characterized Gaussian Markov processes with </span>stationary increments and showed that they arise as </span>asymptotic approximations for stochastic </span>point processes with a random rate such as Polya processes, which can be useful to model over-dispersion and path-dependent behavior in service system arrival processes. Here we provide additional insight into these stochastic processes.</p></div>","PeriodicalId":54682,"journal":{"name":"Operations Research Letters","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139069653","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
An inexact algorithm for stochastic variational inequalities 随机变分不等式的非精确算法
IF 1.1 4区 管理学
Operations Research Letters Pub Date : 2024-01-01 DOI: 10.1016/j.orl.2023.107064
Emelin L. Buscaglia , Pablo A. Lotito , Lisandro A. Parente
{"title":"An inexact algorithm for stochastic variational inequalities","authors":"Emelin L. Buscaglia ,&nbsp;Pablo A. Lotito ,&nbsp;Lisandro A. Parente","doi":"10.1016/j.orl.2023.107064","DOIUrl":"10.1016/j.orl.2023.107064","url":null,"abstract":"<div><p><span>We present a new Progressive Hedging Algorithm to solve Stochastic Variational Inequalities in the formulation introduced by Rockafellar and Wets in 2017, allowing the generated </span>subproblems to be approximately solved with an implementable tolerance condition. Our scheme is based on Hybrid Inexact Proximal Point methods and generalizes the exact algorithm developed by Rockafellar and Sun in 2019, providing stronger convergence results. We also show some numerical experiments in two-stage Nash games.</p></div>","PeriodicalId":54682,"journal":{"name":"Operations Research Letters","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139069713","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 truthful constrained heterogeneous facility location with max-variant cost 论具有最大变异成本的真实受限异构设施定位
IF 1.1 4区 管理学
Operations Research Letters Pub Date : 2024-01-01 DOI: 10.1016/j.orl.2023.107060
Mohammad Lotfi , Alexandros A. Voudouris
{"title":"On truthful constrained heterogeneous facility location with max-variant cost","authors":"Mohammad Lotfi ,&nbsp;Alexandros A. Voudouris","doi":"10.1016/j.orl.2023.107060","DOIUrl":"10.1016/j.orl.2023.107060","url":null,"abstract":"<div><p>We consider a problem where agents have private positions on a line, and public approval preferences over two facilities, and their cost is the maximum distance from their approved facilities. The goal is to decide the facility locations to minimize the total and the max cost, while incentivizing the agents to be truthful. We design a strategyproof mechanism that is simultaneously 11- and 5-approximate for these two objective functions, thus improving the previously best-known bounds of <span><math><mn>2</mn><mi>n</mi><mo>+</mo><mn>1</mn></math></span> and 9.</p></div>","PeriodicalId":54682,"journal":{"name":"Operations Research Letters","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0167637723002018/pdfft?md5=533c0ef6846afe12cb9dce906c7c37bb&pid=1-s2.0-S0167637723002018-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139026824","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
Universally optimal staffing of Erlang-A queues facing uncertain arrival rates 面对不确定到达率的 Erlang-A 队列的普遍最优人员配置
IF 1.1 4区 管理学
Operations Research Letters Pub Date : 2024-01-01 DOI: 10.1016/j.orl.2023.107061
Yaşar Levent Koçağa
{"title":"Universally optimal staffing of Erlang-A queues facing uncertain arrival rates","authors":"Yaşar Levent Koçağa","doi":"10.1016/j.orl.2023.107061","DOIUrl":"10.1016/j.orl.2023.107061","url":null,"abstract":"<div><p><span>In many service systems, the staffing decisions must be made before the arrival rate is known with certainty. Thus, it is more appropriate to consider the arrival rate as a random variable at the time of the staffing decision. Motivated by this observation, we study the staffing problem in a service system modeled as an Erlang-A queue facing a </span><em>random</em> arrival rate. For linear staffing costs, linear waiting costs, and a cost per customer abandonment, we propose a policy that is based on modifying the well-known square-root safety staffing policy to explicitly account for the randomness in the arrival rate. Our primary contribution is to show that our proposed policy is “universally optimal”, i.e., <em>irrespective</em><span><span> of the magnitude of randomness in the arrival rate, the optimality gap between our proposed policy and the exact </span>optimal policy remains bounded as the system size grows large. This is important because earlier performance guarantees for Erlang-A queues either (1) are </span><em>not</em> universal and offer performance guarantees that depend on the magnitude of uncertainty in the arrival rate or (2) are universal but assume a <em>deterministic</em> arrival rate. The practical relevance of this provable robustness is that our proposed policy is a “one-size-fits-all” as it is guaranteed to perform well for <em>all</em> levels of arrival rate uncertainty.</p></div>","PeriodicalId":54682,"journal":{"name":"Operations Research Letters","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139070199","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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