SOLVING MIXED-INTEGER SECOND ORDER CONE PROGRAMS BY GENERALIZED BENDERS DECOMPOSITION

被引：0
|
作者：
Wei, Zhou [1 ,2 ]
Chen, Liang [3 ]
Dai, Yu-hong [3 ,4 ]
机构：
[1] Hebei Univ, Hebei Key Lab Machine Learning & Computat Intellig, Baoding 071002, Peoples R China
[2] Hebei Univ, Coll Math & Informat Sci, Baoding 071002, Peoples R China
[3] Chinese Acad Sci, Acad Math & Syst Sci, LSEC, Beijing 100190, Peoples R China
[4] Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
来源：
JOURNAL OF NONLINEAR AND CONVEX ANALYSIS | 2023年 / 24卷 / 04期
关键词：
Mixed-integer second order cone programming; generalized Benders decomposition; optimal Lagrange multiplier; master problem; ERROR-BOUNDS; PROJECTION ALGORITHMS; OUTER APPROXIMATION; CONVERGENCE; SYSTEMS;
D O I：
暂无
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
This paper is to study a mixed-integer second order cone program (MISOCP) problem and its solution algorithm by generalized Benders decomposition. When fixing the integer variables, we solve several subproblems as well as their dual problems and obtain optimal Lagrange multipliers of subproblems which can be used to establish linear valid Benders cuts and reformulate MISOCP as an equivalent mixed-integer linear program (MILP) master problem. Then we construct a generalized Benders algorithm for finding the optimal solution to MISOCP by solving a sequence of MILP relaxations. The algorithm is proved to terminate after a finite number of steps. Numerical results for the MISOCP instance are presented to show the feasibility of the constructed algorithm in solving MISOCP problems.
引用
收藏
页码：869 / 888
页数：20
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