Novel Optimality Cuts for Two-Stage Stochastic Mixed-Integer Programs The applicability and use of two-stage stochastic mixed-integer programs is well-established, thus calling for efficient decomposition algorithms to solve them. Such algorithms typically rely on optimality cuts to approximate the expected second stage cost function from below. In “A Converging Benders’ Decomposition Algorithm for Mixed-Integer Recourse Models,” van der Laan and Romeijnders derive a new family of optimality cuts that is sufficiently rich to identify the optimal solution of two-stage stochastic mixed-integer programs in general. That is, general mixed-integer decision variables are allowed in both stages, and all data elements are allowed to be random. Moreover, these new optimality cuts require computations that decompose by scenario, and thus, they can be computed efficiently. Van der Laan and Romeijnders demonstrate the potential of their approach on a range of problem instances, including the DCAP instances from SIPLIB.
两阶段随机混合整数规划的适用性和应用已经得到了证实，因此需要有效的分解算法来求解这类规划。这种算法通常依赖于最优切割来从下面近似预期的第二阶段成本函数。在“混合整数追索权模型的收敛弯曲分解算法”中，van der Laan和Romeijnders导出了一个新的最优性切割族，它足够丰富，可以识别一般的两阶段随机混合整数规划的最优解。也就是说，两个阶段都允许使用一般的混合整数决策变量，并且允许所有数据元素都是随机的。此外，这些新的最优性切割需要按场景分解的计算，因此，它们可以有效地计算。Van der Laan和Romeijnders在一系列问题实例(包括SIPLIB中的DCAP实例)上展示了他们的方法的潜力。
{"title":"A Converging Benders’ Decomposition Algorithm for Two-Stage Mixed-Integer Recourse Models","authors":"N. van der Laan, Ward Romeijnders","doi":"10.1287/opre.2021.2223","DOIUrl":"https://doi.org/10.1287/opre.2021.2223","url":null,"abstract":"Novel Optimality Cuts for Two-Stage Stochastic Mixed-Integer Programs The applicability and use of two-stage stochastic mixed-integer programs is well-established, thus calling for efficient decomposition algorithms to solve them. Such algorithms typically rely on optimality cuts to approximate the expected second stage cost function from below. In “A Converging Benders’ Decomposition Algorithm for Mixed-Integer Recourse Models,” van der Laan and Romeijnders derive a new family of optimality cuts that is sufficiently rich to identify the optimal solution of two-stage stochastic mixed-integer programs in general. That is, general mixed-integer decision variables are allowed in both stages, and all data elements are allowed to be random. Moreover, these new optimality cuts require computations that decompose by scenario, and thus, they can be computed efficiently. Van der Laan and Romeijnders demonstrate the potential of their approach on a range of problem instances, including the DCAP instances from SIPLIB.","PeriodicalId":49809,"journal":{"name":"Military Operations Research","volume":"12 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78507565","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}
The pricing problem of vehicle routing problems is strongly NP hard. Many algorithms for finding optimal solutions to various vehicle routing problems rely on a subroutine to solve a so-called pricing problem of a set partitioning formulation. Only exponential time algorithms are known for these pricing problems. Therefore, the set partitioning formulation is oftentimes relaxed at the expense of weaker LP bounds, so that the resulting pricing problem can now be solved using a pseudopolynomial or polynomial time algorithm. In “The Complexity of the Pricing Problem of the Set Partitioning Formulation of Vehicle Routing Problems,” it is proven by Remy Spliet that the pricing problem is strongly NP hard for many different vehicle routing problems. This means that, unless P = NP, no pseudopolynomial or polynomial time algorithm exists for the pricing problem, justifying the common use of relaxations.
{"title":"Technical Note—The Complexity of the Pricing Problem of the Set Partitioning Formulation of Vehicle Routing Problems","authors":"R. Spliet","doi":"10.1287/opre.2023.2481","DOIUrl":"https://doi.org/10.1287/opre.2023.2481","url":null,"abstract":"The pricing problem of vehicle routing problems is strongly NP hard. Many algorithms for finding optimal solutions to various vehicle routing problems rely on a subroutine to solve a so-called pricing problem of a set partitioning formulation. Only exponential time algorithms are known for these pricing problems. Therefore, the set partitioning formulation is oftentimes relaxed at the expense of weaker LP bounds, so that the resulting pricing problem can now be solved using a pseudopolynomial or polynomial time algorithm. In “The Complexity of the Pricing Problem of the Set Partitioning Formulation of Vehicle Routing Problems,” it is proven by Remy Spliet that the pricing problem is strongly NP hard for many different vehicle routing problems. This means that, unless P = NP, no pseudopolynomial or polynomial time algorithm exists for the pricing problem, justifying the common use of relaxations.","PeriodicalId":49809,"journal":{"name":"Military Operations Research","volume":"143 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-05-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76433218","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}
In the Bayesian newsvendor problem, it is known that the optimal decision is always greater than or equal to the myopic decision. As a result, the optimal decision can be expressed as the sum of the myopic decision plus a nonnegative “exploration boost.” In “Bayesian Inventory Control: Accelerated Demand Learning via Exploration Boosts,” Chuang and Kim characterize the form of the exploration boost in terms of basic statistical measures of uncertainty. This characterization expresses in clear terms the way in which the statistical learning and inventory control are jointly optimized; when there is a high degree of parameter uncertainty, inventory levels are boosted to induce a higher chance of observing more sales data to more quickly resolve statistical uncertainty, and as parameter uncertainty resolves, the exploration boost is reduced.
{"title":"Bayesian Inventory Control: Accelerated Demand Learning via Exploration Boosts","authors":"Ya-Tang Chuang, Michael Jong Kim","doi":"10.1287/opre.2023.2467","DOIUrl":"https://doi.org/10.1287/opre.2023.2467","url":null,"abstract":"In the Bayesian newsvendor problem, it is known that the optimal decision is always greater than or equal to the myopic decision. As a result, the optimal decision can be expressed as the sum of the myopic decision plus a nonnegative “exploration boost.” In “Bayesian Inventory Control: Accelerated Demand Learning via Exploration Boosts,” Chuang and Kim characterize the form of the exploration boost in terms of basic statistical measures of uncertainty. This characterization expresses in clear terms the way in which the statistical learning and inventory control are jointly optimized; when there is a high degree of parameter uncertainty, inventory levels are boosted to induce a higher chance of observing more sales data to more quickly resolve statistical uncertainty, and as parameter uncertainty resolves, the exploration boost is reduced.","PeriodicalId":49809,"journal":{"name":"Military Operations Research","volume":"63 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80585005","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}
The paper studies generalization of the secretary problem, where decisions do not have to be made immediately upon applicants’ arrivals. After arriving, each applicant stays in the system for some (random) amount of time and then leaves, whereupon the algorithm has to decide irrevocably whether to select this applicant or not. The arrival and waiting times are drawn from known distributions, and the decision maker’s goal is to maximize the probability of selecting the best applicant overall. The paper characterizes the optimal policy for this setting, showing that when deciding whether to select an applicant, it suffices to know only the time and the number of applicants that have arrived so far. Furthermore, the policy is monotone nondecreasing in the number of applicants seen so far, and, under certain natural conditions, monotone nonincreasing in time. Furthermore, when the number of applicants is large, a single threshold policy is almost optimal.
{"title":"On Hiring Secretaries with Stochastic Departures","authors":"Thomas Kesselheim, Alexandros Psomas, Shai Vardi","doi":"10.1287/opre.2023.2476","DOIUrl":"https://doi.org/10.1287/opre.2023.2476","url":null,"abstract":"The paper studies generalization of the secretary problem, where decisions do not have to be made immediately upon applicants’ arrivals. After arriving, each applicant stays in the system for some (random) amount of time and then leaves, whereupon the algorithm has to decide irrevocably whether to select this applicant or not. The arrival and waiting times are drawn from known distributions, and the decision maker’s goal is to maximize the probability of selecting the best applicant overall. The paper characterizes the optimal policy for this setting, showing that when deciding whether to select an applicant, it suffices to know only the time and the number of applicants that have arrived so far. Furthermore, the policy is monotone nondecreasing in the number of applicants seen so far, and, under certain natural conditions, monotone nonincreasing in time. Furthermore, when the number of applicants is large, a single threshold policy is almost optimal.","PeriodicalId":49809,"journal":{"name":"Military Operations Research","volume":"34 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84677024","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}
T. Bacci, A. Frangioni, C. Gentile, Kostas Tavlaridis-Gyparakis
Mixed-Integer Formulations for Power Production Problems The unit commitment problem is a complex mixed-integer nonlinear program that originates in the field of power production. Although it arises in a monopolistic system, there is still great attention to this problem even in a free-market regime, where it constitutes only a subproblem of larger ones. Historically, it was usually solved by Lagrangian relaxation methods. However, the advances achieved by commercial solvers of mixed-integer (linear and convex) programming problems have made such approaches an attractive option. T. Bacci, A. Frangioni, C. Gentile, and K. Tavlaridis-Gyparakis present the first mixed-integer nonlinear programming formulation with a polynomial number of both variables and constraints that describes the convex hull of the feasible solutions of the unit commitment problem with a single thermal generation unit, comprising all typical constraints and convex power generation costs. Proving that the formulation is exact requires a new result about the convex envelope of specially structured functions that can have independent interest. This new formulation for a single power generation unit is used to derive three new formulations for the general unit commitment problem whose effectiveness has been tested against the state-of-art formulation.
机组承诺问题是一个复杂的混合整数非线性规划问题，起源于电力生产领域。虽然它出现在垄断制度中，但即使在自由市场制度中，这个问题仍然受到高度重视，它只是大问题中的一个子问题。历史上，它通常是用拉格朗日松弛法求解的。然而，混合整数(线性和凸)规划问题的商业求解器所取得的进步使这种方法成为一种有吸引力的选择。T. Bacci, a . Frangioni, C. Gentile和K. Tavlaridis-Gyparakis提出了第一个混合整数非线性规划公式，该公式包含变量和约束的多项式数，描述了包含所有典型约束和凸发电成本的单个火力发电机组的机组承诺问题可行解的凸包。要证明这个公式是精确的，需要一个关于具有独立兴趣的特殊结构函数的凸包络的新结果。利用这一单一发电机组的新公式推导出一般机组承诺问题的三个新公式，并与现有的新公式进行了有效性测试。
{"title":"New Mixed-Integer Nonlinear Programming Formulations for the Unit Commitment Problems with Ramping Constraints","authors":"T. Bacci, A. Frangioni, C. Gentile, Kostas Tavlaridis-Gyparakis","doi":"10.1287/opre.2023.2435","DOIUrl":"https://doi.org/10.1287/opre.2023.2435","url":null,"abstract":"Mixed-Integer Formulations for Power Production Problems The unit commitment problem is a complex mixed-integer nonlinear program that originates in the field of power production. Although it arises in a monopolistic system, there is still great attention to this problem even in a free-market regime, where it constitutes only a subproblem of larger ones. Historically, it was usually solved by Lagrangian relaxation methods. However, the advances achieved by commercial solvers of mixed-integer (linear and convex) programming problems have made such approaches an attractive option. T. Bacci, A. Frangioni, C. Gentile, and K. Tavlaridis-Gyparakis present the first mixed-integer nonlinear programming formulation with a polynomial number of both variables and constraints that describes the convex hull of the feasible solutions of the unit commitment problem with a single thermal generation unit, comprising all typical constraints and convex power generation costs. Proving that the formulation is exact requires a new result about the convex envelope of specially structured functions that can have independent interest. This new formulation for a single power generation unit is used to derive three new formulations for the general unit commitment problem whose effectiveness has been tested against the state-of-art formulation.","PeriodicalId":49809,"journal":{"name":"Military Operations Research","volume":"63 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78210512","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}
Emre Nadar, Mustafa Akan, L. Debo, Alan Scheller-Wolf
The Importance of Considering System Congestion When Acquiring Used Items for Remanufacturing The condition of used items obtained by remanufacturers often varies widely and may only be truly known after an inspection. In “Technical Note–Optimal Procurement in Remanufacturing Systems with Uncertain Used-Item Condition,” Nadar, Akan, Debo, and Scheller-Wolf study the procurement problem by taking into account this pre-inspection uncertainty as well as the quantities of available used items of different quality levels. The authors provide a novel optimal policy structure for a Markov decision process representation of this problem. They prove that the optimal acquisition decision depends on the system congestion level — the total remanufacturing load weighted by the quality levels. Their results show that it becomes less desirable to acquire a used item as the number of available items or the quality level of any available item increases. To prove their results, the authors introduce a new functional characterization that is a relaxation of supermodularity and discrete convexity.
{"title":"Optimal Procurement in Remanufacturing Systems with Uncertain Used-Item Condition","authors":"Emre Nadar, Mustafa Akan, L. Debo, Alan Scheller-Wolf","doi":"10.1287/opre.2023.2483","DOIUrl":"https://doi.org/10.1287/opre.2023.2483","url":null,"abstract":"The Importance of Considering System Congestion When Acquiring Used Items for Remanufacturing The condition of used items obtained by remanufacturers often varies widely and may only be truly known after an inspection. In “Technical Note–Optimal Procurement in Remanufacturing Systems with Uncertain Used-Item Condition,” Nadar, Akan, Debo, and Scheller-Wolf study the procurement problem by taking into account this pre-inspection uncertainty as well as the quantities of available used items of different quality levels. The authors provide a novel optimal policy structure for a Markov decision process representation of this problem. They prove that the optimal acquisition decision depends on the system congestion level — the total remanufacturing load weighted by the quality levels. Their results show that it becomes less desirable to acquire a used item as the number of available items or the quality level of any available item increases. To prove their results, the authors introduce a new functional characterization that is a relaxation of supermodularity and discrete convexity.","PeriodicalId":49809,"journal":{"name":"Military Operations Research","volume":"97 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80534251","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}
When are Coupled Networked Markets Prone to Sudden Collapse? Many important financial instruments are traded in large networked markets, whose fragility played a role in the Great Financial Crisis. In “Exit Spirals in Coupled Networked Markets,” Aymanns, Georg, and Golub study strategic market participation to show that fragility is exacerbated when several networked markets are coupled, so that activity in one market facilitates participation in others. Such coupling occurs, for example, when participants use relationships in one market to borrow funds to trade in others. The authors ask when market participation is prone to sudden collapse in an exit spiral. They explain when such exit spirals emerge and find that market coupling is a pervasive cause of fragility, creating exit spirals even between networks that are individually robust. The fragility of coupled markets can be mitigated if one of two coupled markets becomes centralized or if links become more correlated across markets.
{"title":"Exit Spirals in Coupled Networked Markets","authors":"Christoph Aymanns, Co-Pierre Georg, B. Golub","doi":"10.1287/opre.2023.2439","DOIUrl":"https://doi.org/10.1287/opre.2023.2439","url":null,"abstract":"When are Coupled Networked Markets Prone to Sudden Collapse? Many important financial instruments are traded in large networked markets, whose fragility played a role in the Great Financial Crisis. In “Exit Spirals in Coupled Networked Markets,” Aymanns, Georg, and Golub study strategic market participation to show that fragility is exacerbated when several networked markets are coupled, so that activity in one market facilitates participation in others. Such coupling occurs, for example, when participants use relationships in one market to borrow funds to trade in others. The authors ask when market participation is prone to sudden collapse in an exit spiral. They explain when such exit spirals emerge and find that market coupling is a pervasive cause of fragility, creating exit spirals even between networks that are individually robust. The fragility of coupled markets can be mitigated if one of two coupled markets becomes centralized or if links become more correlated across markets.","PeriodicalId":49809,"journal":{"name":"Military Operations Research","volume":"23 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79688094","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}
Both walk-in and online customers appear in many service systems such as restaurants. Online customers are often given a target time for pick up, and the quality of the food/beverage can degrade if it is ready before the arrival of online customers. This distinctive feature brings essential difficulties in the analysis and control of such systems. In “Technical Note: Asymptotically Optimal Control of Omnichannel Service Systems with Pick-up Guarantees,” Gao, Huang, and Zhang study the optimal control problem of such service systems based on a two-class single server queueing model. The paper proposes a nearly-optimal policy that keeps the server idle when the queue of online customers drops below a threshold and there are no walk-in customers.
{"title":"Technical Note—Asymptotically Optimal Control of Omnichannel Service Systems with Pick-up Guarantees","authors":"Xuefeng Gao, Jun-fei Huang, Jiheng Zhang","doi":"10.1287/opre.2022.2416","DOIUrl":"https://doi.org/10.1287/opre.2022.2416","url":null,"abstract":"Both walk-in and online customers appear in many service systems such as restaurants. Online customers are often given a target time for pick up, and the quality of the food/beverage can degrade if it is ready before the arrival of online customers. This distinctive feature brings essential difficulties in the analysis and control of such systems. In “Technical Note: Asymptotically Optimal Control of Omnichannel Service Systems with Pick-up Guarantees,” Gao, Huang, and Zhang study the optimal control problem of such service systems based on a two-class single server queueing model. The paper proposes a nearly-optimal policy that keeps the server idle when the queue of online customers drops below a threshold and there are no walk-in customers.","PeriodicalId":49809,"journal":{"name":"Military Operations Research","volume":"29 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88766669","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}
Frank E. Curtis, D. Molzahn, Shenyinying Tu, A. Wächter, Ermin Wei, Elizabeth Wong
The article “A Decomposition Algorithm with Fast Identification of Critical Contingencies for Large-Scale Security-Constrained AC-OPF” presents the decomposition algorithm used by Team GO-SNIP for the ARPA-E Grid Optimization (GO) Competition Challenge 1, held from November 2018 through October 2019. The algorithm involves unique contingency ranking and evaluation strategies for determining the important contingencies to include in a master problem that approximates the original large-scale security-constrained problem. It also involves efficient strategies for handling the complementarity constraints that appear in the model and for handling the arising degeneracies. Software implementation details are described, and the results of an extensive set of numerical experiments are provided to illustrate the effectiveness of each of the used techniques. Team GO-SNIP received a second-place finish in Challenge 1 of the Go Competition.
{"title":"A Decomposition Algorithm with Fast Identification of Critical Contingencies for Large-Scale Security-Constrained AC-OPF","authors":"Frank E. Curtis, D. Molzahn, Shenyinying Tu, A. Wächter, Ermin Wei, Elizabeth Wong","doi":"10.1287/opre.2023.2453","DOIUrl":"https://doi.org/10.1287/opre.2023.2453","url":null,"abstract":"The article “A Decomposition Algorithm with Fast Identification of Critical Contingencies for Large-Scale Security-Constrained AC-OPF” presents the decomposition algorithm used by Team GO-SNIP for the ARPA-E Grid Optimization (GO) Competition Challenge 1, held from November 2018 through October 2019. The algorithm involves unique contingency ranking and evaluation strategies for determining the important contingencies to include in a master problem that approximates the original large-scale security-constrained problem. It also involves efficient strategies for handling the complementarity constraints that appear in the model and for handling the arising degeneracies. Software implementation details are described, and the results of an extensive set of numerical experiments are provided to illustrate the effectiveness of each of the used techniques. Team GO-SNIP received a second-place finish in Challenge 1 of the Go Competition.","PeriodicalId":49809,"journal":{"name":"Military Operations Research","volume":"29 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-04-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85589231","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}
Properly defining the center of a set has been a longstanding question in applied mathematics, with implications in numerical geometry, physics, and optimization algorithms. Minkowski centers are one such definition, whose theoretical benefits are numerous and well documented. In this paper, we revisit the advantages of Minkowski centers from a computational, rather than theoretical, perspective. First, we show that Minkowski centers are solutions to a robust optimization problem. Under this lens, we then provide computationally tractable reformulations or approximations for a series of sets, including polyhedra, polyhedral projections, and intersections of ellipsoids. Computationally, we illustrate that Minkowski centers are viable alternatives to other centers, such as Chebyshev or analytic centers, and can speed up the convergence of numerical algorithms like hit-and-run and cutting-plane methods. We hope our work sheds new and practical light on Minkowski centers and exposes their potential benefits as a computational tool.
{"title":"Minkowski Centers via Robust Optimization: Computation and Applications","authors":"D. den Hertog, J. Pauphilet, Mohamed Yahya Soali","doi":"10.1287/opre.2023.2448","DOIUrl":"https://doi.org/10.1287/opre.2023.2448","url":null,"abstract":"Properly defining the center of a set has been a longstanding question in applied mathematics, with implications in numerical geometry, physics, and optimization algorithms. Minkowski centers are one such definition, whose theoretical benefits are numerous and well documented. In this paper, we revisit the advantages of Minkowski centers from a computational, rather than theoretical, perspective. First, we show that Minkowski centers are solutions to a robust optimization problem. Under this lens, we then provide computationally tractable reformulations or approximations for a series of sets, including polyhedra, polyhedral projections, and intersections of ellipsoids. Computationally, we illustrate that Minkowski centers are viable alternatives to other centers, such as Chebyshev or analytic centers, and can speed up the convergence of numerical algorithms like hit-and-run and cutting-plane methods. We hope our work sheds new and practical light on Minkowski centers and exposes their potential benefits as a computational tool.","PeriodicalId":49809,"journal":{"name":"Military Operations Research","volume":"65 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84238978","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}
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