论广义幂锥的最小扩展表示

IF 2.6 1区数学 Q1 MATHEMATICS, APPLIED

SIAM Journal on Optimization Pub Date : 2024-09-10 DOI:10.1137/23m1617205

Víctor Blanco, Miguel Martínez-Antón

{"title":"论广义幂锥的最小扩展表示","authors":"Víctor Blanco, Miguel Martínez-Antón","doi":"10.1137/23m1617205","DOIUrl":null,"url":null,"abstract":"SIAM Journal on Optimization, Volume 34, Issue 3, Page 3088-3111, September 2024. <br/> Abstract. In this paper, we analyze minimal representations of [math]-power cones as simpler cones. We derive some new results on the complexity of the representations, and we provide a procedure to construct a minimal representation by means of second order cones in case [math] and [math] are rational. The construction is based on the identification of the cones with a graph, the mediated graph. Then, we develop a mixed integer linear optimization formulation to obtain the optimal mediated graph, and then the minimal representation. We present the results of a series of computational experiments in order to analyze the computational performance of the approach, both to obtain the representation and its incorporation into a practical conic optimization model that arises in facility location.","PeriodicalId":49529,"journal":{"name":"SIAM Journal on Optimization","volume":"178 1","pages":""},"PeriodicalIF":2.6000,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On Minimal Extended Representations of Generalized Power Cones\",\"authors\":\"Víctor Blanco, Miguel Martínez-Antón\",\"doi\":\"10.1137/23m1617205\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"SIAM Journal on Optimization, Volume 34, Issue 3, Page 3088-3111, September 2024. <br/> Abstract. In this paper, we analyze minimal representations of [math]-power cones as simpler cones. We derive some new results on the complexity of the representations, and we provide a procedure to construct a minimal representation by means of second order cones in case [math] and [math] are rational. The construction is based on the identification of the cones with a graph, the mediated graph. Then, we develop a mixed integer linear optimization formulation to obtain the optimal mediated graph, and then the minimal representation. We present the results of a series of computational experiments in order to analyze the computational performance of the approach, both to obtain the representation and its incorporation into a practical conic optimization model that arises in facility location.\",\"PeriodicalId\":49529,\"journal\":{\"name\":\"SIAM Journal on Optimization\",\"volume\":\"178 1\",\"pages\":\"\"},\"PeriodicalIF\":2.6000,\"publicationDate\":\"2024-09-10\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"SIAM Journal on Optimization\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1137/23m1617205\",\"RegionNum\":1,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"SIAM Journal on Optimization","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1137/23m1617205","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}

引用次数: 0

摘要

SIAM 优化期刊》，第 34 卷第 3 期，第 3088-3111 页，2024 年 9 月。摘要在本文中，我们分析了[math]-幂锥作为简锥的最小表示。我们得出了一些关于表示复杂性的新结果，并提供了在 [math] 和 [math] 都是有理数的情况下通过二阶圆锥构造最小表示的过程。该构造基于锥形与图形（即中介图）的识别。然后，我们开发了一种混合整数线性优化公式，以获得最佳中介图，进而获得最小表示。我们展示了一系列计算实验的结果，以分析该方法的计算性能，包括获得表示法以及将其纳入设施选址中出现的实际圆锥优化模型。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

On Minimal Extended Representations of Generalized Power Cones

SIAM Journal on Optimization, Volume 34, Issue 3, Page 3088-3111, September 2024.
Abstract. In this paper, we analyze minimal representations of [math]-power cones as simpler cones. We derive some new results on the complexity of the representations, and we provide a procedure to construct a minimal representation by means of second order cones in case [math] and [math] are rational. The construction is based on the identification of the cones with a graph, the mediated graph. Then, we develop a mixed integer linear optimization formulation to obtain the optimal mediated graph, and then the minimal representation. We present the results of a series of computational experiments in order to analyze the computational performance of the approach, both to obtain the representation and its incorporation into a practical conic optimization model that arises in facility location.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

SIAM Journal on Optimization 数学-应用数学

CiteScore

5.30

自引率

9.70%

发文量

101

审稿时长

6-12 weeks

期刊介绍： The SIAM Journal on Optimization contains research articles on the theory and practice of optimization. The areas addressed include linear and quadratic programming, convex programming, nonlinear programming, complementarity problems, stochastic optimization, combinatorial optimization, integer programming, and convex, nonsmooth and variational analysis. Contributions may emphasize optimization theory, algorithms, software, computational practice, applications, or the links between these subjects.