{"title":"混合整数线性方程组全局求解的分解方法","authors":"Kaizhao Sun, Mou Sun, Wotao Yin","doi":"10.1137/22m1487321","DOIUrl":null,"url":null,"abstract":"SIAM Journal on Optimization, Volume 34, Issue 2, Page 1206-1235, June 2024. <br/> Abstract. This paper introduces two decomposition-based methods for two-block mixed-integer linear programs (MILPs), which aim to take advantage of separable structures of the original problem by solving a sequence of lower-dimensional MILPs. The first method is based on the [math]-augmented Lagrangian method, and the second one is based on a modified alternating direction method of multipliers. In the presence of certain block-angular structures, both methods create parallel subproblems in one block of variables and add nonconvex cuts to update the other block; they converge to globally optimal solutions of the original MILP under proper conditions. Numerical experiments on three classes of MILPs demonstrate the advantages of the proposed methods on structured problems over the state-of-the-art MILP solvers.","PeriodicalId":49529,"journal":{"name":"SIAM Journal on Optimization","volume":null,"pages":null},"PeriodicalIF":2.6000,"publicationDate":"2024-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Decomposition Methods for Global Solution of Mixed-Integer Linear Programs\",\"authors\":\"Kaizhao Sun, Mou Sun, Wotao Yin\",\"doi\":\"10.1137/22m1487321\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"SIAM Journal on Optimization, Volume 34, Issue 2, Page 1206-1235, June 2024. <br/> Abstract. This paper introduces two decomposition-based methods for two-block mixed-integer linear programs (MILPs), which aim to take advantage of separable structures of the original problem by solving a sequence of lower-dimensional MILPs. The first method is based on the [math]-augmented Lagrangian method, and the second one is based on a modified alternating direction method of multipliers. In the presence of certain block-angular structures, both methods create parallel subproblems in one block of variables and add nonconvex cuts to update the other block; they converge to globally optimal solutions of the original MILP under proper conditions. Numerical experiments on three classes of MILPs demonstrate the advantages of the proposed methods on structured problems over the state-of-the-art MILP solvers.\",\"PeriodicalId\":49529,\"journal\":{\"name\":\"SIAM Journal on Optimization\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":2.6000,\"publicationDate\":\"2024-04-01\",\"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/10.1137/22m1487321\",\"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/10.1137/22m1487321","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
Decomposition Methods for Global Solution of Mixed-Integer Linear Programs
SIAM Journal on Optimization, Volume 34, Issue 2, Page 1206-1235, June 2024. Abstract. This paper introduces two decomposition-based methods for two-block mixed-integer linear programs (MILPs), which aim to take advantage of separable structures of the original problem by solving a sequence of lower-dimensional MILPs. The first method is based on the [math]-augmented Lagrangian method, and the second one is based on a modified alternating direction method of multipliers. In the presence of certain block-angular structures, both methods create parallel subproblems in one block of variables and add nonconvex cuts to update the other block; they converge to globally optimal solutions of the original MILP under proper conditions. Numerical experiments on three classes of MILPs demonstrate the advantages of the proposed methods on structured problems over the state-of-the-art MILP solvers.
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.