混合整数线性方程组全局求解的分解方法

IF 2.6 1区 数学 Q1 MATHEMATICS, APPLIED SIAM Journal on Optimization Pub Date : 2024-04-01 DOI:10.1137/22m1487321
Kaizhao Sun, Mou Sun, Wotao Yin
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引用次数: 0

摘要

SIAM 优化期刊》,第 34 卷第 2 期,第 1206-1235 页,2024 年 6 月。 摘要本文介绍了两种基于分解的两块混合整数线性程序(MILPs)方法,旨在通过求解一系列低维 MILPs 来利用原问题的可分离结构。第一种方法基于[math]增量拉格朗日法,第二种方法基于改进的乘法交替方向法。在存在某些块-角结构的情况下,这两种方法都能在一个变量块中创建并行子问题,并添加非凸切口来更新另一个变量块;在适当条件下,它们都能收敛到原始 MILP 的全局最优解。对三类 MILP 的数值实验表明,与最先进的 MILP 求解器相比,建议的方法在结构化问题上更具优势。
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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.
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来源期刊
SIAM Journal on Optimization
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.
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