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Decomposition-Invariant Pairwise Frank-Wolfe Algorithm for Constrained Multiobjective Optimization 用于受限多目标优化的分解-不变配对弗兰克-沃尔夫算法
arXiv - MATH - Optimization and Control Pub Date : 2024-09-07 DOI: arxiv-2409.04671
Zhuoxin Fan, Liping Tang
{"title":"Decomposition-Invariant Pairwise Frank-Wolfe Algorithm for Constrained Multiobjective Optimization","authors":"Zhuoxin Fan, Liping Tang","doi":"arxiv-2409.04671","DOIUrl":"https://doi.org/arxiv-2409.04671","url":null,"abstract":"Recently the away-step Frank-Wolfe algoritm for constrained multiobjective\u0000optimization has been shown linear convergence rate over a polytope which is\u0000generated by finite points set. In this paper we design a\u0000decomposition-invariant pairwise frank-wolfe algorithm for multiobjective\u0000optimization that the feasible region is an arbitrary bounded polytope. We\u0000prove it has linear convergence rate of the whole sequence to a pareto optimal\u0000solution under strongly convexity without other assumptions.","PeriodicalId":501286,"journal":{"name":"arXiv - MATH - Optimization and Control","volume":"64 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142212443","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 $Δ$-evaluation function for column permutation problems 列排列问题的 $Δ$ 评估函数
arXiv - MATH - Optimization and Control Pub Date : 2024-09-07 DOI: arxiv-2409.04926
Júnior R. Lima, Viníicius Gandra M. Santos, Marco Antonio M. Carvalho
{"title":"A $Δ$-evaluation function for column permutation problems","authors":"Júnior R. Lima, Viníicius Gandra M. Santos, Marco Antonio M. Carvalho","doi":"arxiv-2409.04926","DOIUrl":"https://doi.org/arxiv-2409.04926","url":null,"abstract":"In this study, a new $Delta$-evaluation method is introduced for solving a\u0000column permutation problem defined on a sparse binary matrix with the\u0000consecutive ones property. This problem models various $mathcal{NP}$-hard\u0000problems in graph theory and industrial manufacturing contexts. The\u0000computational experiments compare the processing time of the\u0000$Delta$-evaluation method with two other methods used in well-known local\u0000search procedures. The study considers a comprehensive set of instances of\u0000well-known problems, such as Gate Matrix Layout and Minimization of Open\u0000Stacks. The proposed evaluation method is generally competitive and\u0000particularly useful for large and dense instances. It can be easily integrated\u0000into local search and metaheuristic algorithms to improve solutions without\u0000significantly increasing processing time.","PeriodicalId":501286,"journal":{"name":"arXiv - MATH - Optimization and Control","volume":"12 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142212469","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
Geometric commutation principle for weakly spectral sets in Euclidean Jordan algebras 欧几里得约旦代数中弱谱集的几何换向原理
arXiv - MATH - Optimization and Control Pub Date : 2024-09-07 DOI: arxiv-2409.04712
Juyoung Jeong
{"title":"Geometric commutation principle for weakly spectral sets in Euclidean Jordan algebras","authors":"Juyoung Jeong","doi":"arxiv-2409.04712","DOIUrl":"https://doi.org/arxiv-2409.04712","url":null,"abstract":"A geometric commutation principle in Euclidean Jordan algebra, recently\u0000proved by Gowda, says that, for any spectral set $E$ in a Euclidean Jordan\u0000algebra $V$ and $a in E$, $a$ strongly operator commutes with every element in\u0000the normal cone $N_E(a)$. Further, it can be used to establish strong operator\u0000commutativity relations in certain optimization problems. Knowing that every\u0000spectral sets are special cases of broader class of weakly spectral sets, we\u0000prove an analog of a geometric commutation principle for weakly spectral sets\u0000and study its consequences and applications.","PeriodicalId":501286,"journal":{"name":"arXiv - MATH - Optimization and Control","volume":"19 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142212442","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
Non-concave utility maximization problem with transaction costs and a given consistent price system 具有交易成本和给定一致价格体系的非凹式效用最大化问题
arXiv - MATH - Optimization and Control Pub Date : 2024-09-06 DOI: arxiv-2409.04506
Lingqi Gu, Yiqing Lin
{"title":"Non-concave utility maximization problem with transaction costs and a given consistent price system","authors":"Lingqi Gu, Yiqing Lin","doi":"arxiv-2409.04506","DOIUrl":"https://doi.org/arxiv-2409.04506","url":null,"abstract":"We investigate expected utility maximization problems from the terminal\u0000liquidation value in continuous time in markets with transaction costs and one\u0000fixed consistent price system, where a non-concave utility function is defined\u0000on the positive half real line. The sufficient conditions are given by the\u0000convex conjugate of the utility function, then the existence of the optimizer\u0000is proved by a maximizing sequence. Finally, we show that the value function of\u0000the envelope of the utility function and the concave envelope of the value\u0000function are coincide.","PeriodicalId":501286,"journal":{"name":"arXiv - MATH - Optimization and Control","volume":"284 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142212448","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
Impact of Transit on Mobility, Equity, and Economy in the Chicago Metropolitan Region 公交对芝加哥大都会地区流动性、公平性和经济的影响
arXiv - MATH - Optimization and Control Pub Date : 2024-09-06 DOI: arxiv-2409.04568
Omer Verbas, Taner Cokyasar, Seamus Joyce-Johnson, Scott Wainwright, Maeve Coates, Aymeric Rousseau, Jim Aloisi, Anson Stewart, Joshua Auld
{"title":"Impact of Transit on Mobility, Equity, and Economy in the Chicago Metropolitan Region","authors":"Omer Verbas, Taner Cokyasar, Seamus Joyce-Johnson, Scott Wainwright, Maeve Coates, Aymeric Rousseau, Jim Aloisi, Anson Stewart, Joshua Auld","doi":"arxiv-2409.04568","DOIUrl":"https://doi.org/arxiv-2409.04568","url":null,"abstract":"Transit is essential for urban transportation and achieving net-zero targets.\u0000In urban areas like the Chicago Metropolitan Region, transit enhances mobility\u0000and connects people, fostering a dynamic economy. To quantify the mobility and\u0000selected economic impacts of transit, we use a novel agent-based simulation\u0000model POLARIS to compare baseline service against a scenario in which transit\u0000is completely removed. The transit-removal scenario assumes higher car\u0000ownership and results in higher traffic congestion, numerous activity\u0000cancellations, and economic decline. In this scenario, average travel times\u0000increase by 14.2% regionally and 34.7% within the City of Chicago. The\u0000resulting congestion causes significant activity cancellations despite\u0000increased car ownership: 11.8% of non-work and 2.8% of work/school activities\u0000regionally, totaling an 8.6% overall cancellation rate. In the city, non-work\u0000cancellations would reach 26.9%, and work/school cancellations 7.3%, leading to\u0000a 19.9% overall cancellation rate. The impact varies between groups. Women and\u0000lower-income individuals are more likely to cancel activities than men and\u0000higher-income groups. Women account for 53.7% of non-work and 53.0% of total\u0000cancellations. The lowest 40% income group experiences 50.2% of non-work and\u000048.0% of overall cancellations. Combined, activity cancellations, travel time\u0000losses, and increased car ownership cost the region $35.4 billion. With annual\u0000public transit funding at $2.7 billion, the ratio is 13 to 1, underscoring\u0000transit's critical role in mobility, equity, and economic health.","PeriodicalId":501286,"journal":{"name":"arXiv - MATH - Optimization and Control","volume":"58 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142212445","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
Second Order Stein-Variational Dynamic Optimization 二阶斯坦因变量动态优化
arXiv - MATH - Optimization and Control Pub Date : 2024-09-06 DOI: arxiv-2409.04644
Yuichiro Aoyama, Peter Lehmamnn, Evangelos A. Theodorou
{"title":"Second Order Stein-Variational Dynamic Optimization","authors":"Yuichiro Aoyama, Peter Lehmamnn, Evangelos A. Theodorou","doi":"arxiv-2409.04644","DOIUrl":"https://doi.org/arxiv-2409.04644","url":null,"abstract":"We present a novel second-order trajectory optimization algorithm based on\u0000Stein Variational Newton's Method and Maximum Entropy Differential Dynamic\u0000Programming. The proposed algorithm, called Stein Variational Differential\u0000Dynamic Programming, is a kernel-based extension of Maximum Entropy\u0000Differential Dynamic Programming that combines the best of the two worlds of\u0000sampling-based and gradient-based optimization. The resulting algorithm avoids\u0000known drawbacks of gradient-based dynamic optimization in terms of getting\u0000stuck to local minima, while it overcomes limitations of sampling-based\u0000stochastic optimization in terms of introducing undesirable stochasticity when\u0000applied in online fashion. To test the efficacy of the proposed algorithm,\u0000experiments are performed for both trajectory optimization and model predictive\u0000control. The experiments include comparisons with unimodal and multimodal\u0000Maximum Entropy Differential Dynamic Programming as well as Model Predictive\u0000Path Integral Control and its multimodal and Stein Variational extensions. The\u0000results demonstrate the superior performance of the proposed algorithms and\u0000confirm the hypothesis that there is a middle ground between sampling and\u0000gradient-based optimization that is indeed beneficial for the purposes of\u0000dynamic optimization. This middle ground consists of different mechanisms that\u0000combine sampling with gradient-based optimization. In this paper, we\u0000investigate these different mechanisms and show their benefits in dealing with\u0000non-convex dynamic optimization problems found in trajectory optimization and\u0000model predictive control.","PeriodicalId":501286,"journal":{"name":"arXiv - MATH - Optimization and Control","volume":"106 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142212444","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
The Strength of Fuel Refueling Location Problem Formulations 加油地点问题公式的强度
arXiv - MATH - Optimization and Control Pub Date : 2024-09-06 DOI: arxiv-2409.04554
Nagisa Sugishita, Margarida Carvalho, Ribal Atallah
{"title":"The Strength of Fuel Refueling Location Problem Formulations","authors":"Nagisa Sugishita, Margarida Carvalho, Ribal Atallah","doi":"arxiv-2409.04554","DOIUrl":"https://doi.org/arxiv-2409.04554","url":null,"abstract":"The Fuel Refueling Location Problem (FRLP) is a stylized model for\u0000determining the optimal siting of refueling stations for vehicles with limited\u0000travel ranges, such as hydrogen fuel cell vehicles and electric vehicles. This\u0000problem becomes particularly relevant when the goal is to facilitate\u0000long-distance travel using these vehicles. A variant of the FRLP, known as the\u0000Deviation Fuel Refueling Location Problem, accounts for the possibility that\u0000drivers may deviate from their preferred routes to ensure sufficient fuel or\u0000charging to complete their trips. While solution techniques based on various\u0000mathematical programming formulations have been thoroughly explored for these\u0000problems, there is a lack of theoretical insights into the relationships and\u0000strengths of these formulations. In this work, we study formulations of these\u0000problems used in the literature and compare their strengths in terms of linear\u0000programming relaxations. Furthermore, we explore approaches to tighten the\u0000formulations.","PeriodicalId":501286,"journal":{"name":"arXiv - MATH - Optimization and Control","volume":"48 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142212447","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
QUBO formulation for the Snake-in-the-box and Coil-in-the-box problems 箱中蛇和箱中线圈问题的 QUBO 方案
arXiv - MATH - Optimization and Control Pub Date : 2024-09-05 DOI: arxiv-2409.04476
Federico Fuidio, Eduardo Canale, Rafael Sotelo
{"title":"QUBO formulation for the Snake-in-the-box and Coil-in-the-box problems","authors":"Federico Fuidio, Eduardo Canale, Rafael Sotelo","doi":"arxiv-2409.04476","DOIUrl":"https://doi.org/arxiv-2409.04476","url":null,"abstract":"This paper present the first QUBO formulations for the Snake-in-the-box\u0000(SITB) and Coil-in-the-box (CITB) problems. Both formulations are also capable\u0000of solving the NP-Hard problems of Maximum induced path and Maximum induced\u0000cylce respectively. In the process we also found a new QUBO formulation for the\u0000Maximum Common Induced Sub-graph problem. We proved the correctness of our\u0000formulations for the SITB, CITB and Maximum Common Sub-graph problem, and\u0000tested the formulations of the SITB and CITB in both classical and quantum\u0000solvers, being able to get the best solution for up to 5 dimensions.","PeriodicalId":501286,"journal":{"name":"arXiv - MATH - Optimization and Control","volume":"30 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142212467","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
Quadratic optimal transportation problem with a positive semi definite structure on the cost function 成本函数具有正半定结构的二次优化运输问题
arXiv - MATH - Optimization and Control Pub Date : 2024-08-09 DOI: arxiv-2408.05161
Seonghyeon Jeong
{"title":"Quadratic optimal transportation problem with a positive semi definite structure on the cost function","authors":"Seonghyeon Jeong","doi":"arxiv-2408.05161","DOIUrl":"https://doi.org/arxiv-2408.05161","url":null,"abstract":"Optimal transportation problem seeks for a coupling $pi$ of two probability\u0000measures $mu$ and $nu$ which minimize the total cost $int c dpi$, which is\u0000linear in $pi$. In this paper, we introduce a variation of optimal\u0000transportation problem which we call quadratic transportation problem that\u0000considers a total cost $iint c dpi dpi$ which is quadratic in $pi$. We\u0000compare this problem with other variations of optimal transportation problem,\u0000and prove some properties of the solutions to the problem. Then, we introduce\u0000squared cost function, which let us consider the total cost $iint c dpi dpi$\u0000as a positive semi-definite bilinear operator on probability measures, and show\u0000Kantorovich duality formula when we have a squared cost function.","PeriodicalId":501286,"journal":{"name":"arXiv - MATH - Optimization and Control","volume":"26 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141947474","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 Vectorized Positive Semidefinite Penalty Method for Unconstrained Binary Quadratic Programming 无约束二元二次编程的矢量化正半有限惩罚法
arXiv - MATH - Optimization and Control Pub Date : 2024-08-09 DOI: arxiv-2408.04875
Xinyue Huo, Ran Gu
{"title":"A Vectorized Positive Semidefinite Penalty Method for Unconstrained Binary Quadratic Programming","authors":"Xinyue Huo, Ran Gu","doi":"arxiv-2408.04875","DOIUrl":"https://doi.org/arxiv-2408.04875","url":null,"abstract":"The unconstrained binary quadratic programming (UBQP) problem is a class of\u0000problems of significant importance in many practical applications, such as in\u0000combinatorial optimization, circuit design, and other fields. The positive\u0000semidefinite penalty (PSDP) method originated from research on semidefinite\u0000relaxation, where the introduction of an exact penalty function improves the\u0000efficiency and accuracy of problem solving. In this paper, we propose a\u0000vectorized PSDP method for solving the UBQP problem, which optimizes\u0000computational efficiency by vectorizing matrix variables within a PSDP\u0000framework. Algorithmic enhancements in penalty updating and initialization are\u0000implemented, along with the introduction of two algorithms that integrate the\u0000proximal point algorithm and the projection alternating BB method for\u0000subproblem resolution. Properties of the penalty function and algorithm\u0000convergence are analyzed. Numerical experiments show the superior performance\u0000of the method in providing high-quality solutions and satisfactory solution\u0000times compared to the semidefinite relaxation method and other established\u0000methods.","PeriodicalId":501286,"journal":{"name":"arXiv - MATH - Optimization and Control","volume":"2013 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141947481","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
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