On Solving Nonsmooth Mixed-Integer Nonlinear Programming Problems by Outer Approximation and Generalized Benders Decomposition

被引：7
作者：
Wei, Zhou [1 ]
Ali, M. Montaz [2 ]
Xu, Liang [3 ]
Zeng, Bo [3 ]
Yao, Jen-Chih [4 ,5 ]
机构：
[1] Yunnan Univ, Dept Math, Kunming 650091, Yunnan, Peoples R China
[2] Univ Witwatersrand, Sch Comp Sci & Appl Math, ZA-2050 Johannesburg, South Africa
[3] Univ Pittsburgh, Dept Ind Engn, Pittsburgh, PA 15261 USA
[4] Zhejiang Normal Univ, Dept Math, Jinhua 321004, Peoples R China
[5] China Med Univ, China Med Univ Hosp, Res Ctr Interneural Comp, Taichung 40402, Taiwan
来源：
JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS | 2019年 / 181卷 / 03期
基金：
美国国家科学基金会;
关键词：
Mixed-integer nonlinear programming; Outer approximation; Generalized Benders decomposition; Subgradient; Master program; 90C11; 90C25; 90C30; CUTTING-PLANE METHOD;
D O I：
10.1007/s10957-019-01499-7
中图分类号：
C93 [管理学]; O22 [运筹学];
学科分类号：
070105 ; 12 ; 1201 ; 1202 ; 120202 ;
摘要：
In this paper, we mainly study nonsmooth mixed-integer nonlinear programming problems and solution algorithms by outer approximation and generalized Benders decomposition. Outer approximation and generalized Benders algorithms are provided to solve these problems with nonsmooth convex functions and with conic constraint, respectively. We illustrate these two algorithms by providing detailed procedure of solving several examples. The numerical examples show that outer approximation and generalized Benders decomposition provide a feasible alternative for solving such problems without differentiability.
引用
收藏
页码：840 / 863
页数：24
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