{"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":null,"pages":null},"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}
引用次数: 0
Abstract
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.
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.
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