Extended cutting plane method for a class of nonsmooth nonconvex MINLP problems

被引：18

作者：

Eronen, Ville-Pekka ^{[1
]}

Makela, Marko M. ^{[1
]}

Westerlund, Tapio ^{[2
]}

机构：

[1] Univ Turku, Dept Math & Stat, Turku, Finland

[2] Abo Akad Univ, Proc Design & Syst Engn Lab, Turku, Finland

来源：

OPTIMIZATION | 2015年 / 64卷 / 03期

基金：

芬兰科学院;

关键词：

generalized convexity; mixed-integer programming; pseudoconvex function; alpha ECP; nonsmooth optimization; nonsmooth MINLP; subgradient; extended cutting plane algorithm; 26A27; 90C56; 90C11; 90C26; INTEGER NONLINEAR PROGRAMS; OUTER-APPROXIMATION; ALGORITHM;

D O I：

10.1080/02331934.2013.796473

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 article, a generalization of the ECP algorithm to cover a class of nondifferentiable Mixed-Integer NonLinear Programming problems is studied. In the generalization constraint functions are required to be -pseudoconvex instead of pseudoconvex functions. This enables the functions to be nonsmooth. The objective function is first assumed to be linear but also -pseudoconvex case is considered. Furthermore, the gradients used in the ECP algorithm are replaced by the subgradients of Clarke subdifferential. With some additional assumptions, the resulting algorithm shall be proven to converge to a global minimum.

引用

页码：641 / 661

页数：21

共 11 条

[1]

[Anonymous], 1992, Nonsmooth Optimization: Analysis and Algorithms with Applications to Optimal Control

[2]

[Anonymous], COMPUT CHEM ENG

[3]

Clarke F. H., 1983, OPTIMIZATION NONSMOO

[4] AN OUTER-APPROXIMATION ALGORITHM FOR A CLASS OF MIXED-INTEGER NONLINEAR PROGRAMS [J].