Optimality conditions in global optimization and their applications

被引：20

作者：

Rubinov, A. M. ^{[1
]}

Wu, Z. Y. ^{[1
]}

机构：

[1] Univ Ballarat, Sch Informat Technol & Math Sci, Ballarat, Vic 3353, Australia

来源：

MATHEMATICAL PROGRAMMING | 2009年 / 120卷 / 01期

关键词：

Global optimization; Necessary and sufficient conditions; Abstract convexity; Inequalities;

D O I：

10.1007/s10107-007-0142-4

中图分类号：

TP31 [计算机软件];

学科分类号：

081202 ; 0835 ;

摘要：

In this paper we derive necessary and sufficient conditions for some problems of global minimization. Our approach is based on methods of abstract convexity: we use a representation of an upper semicontinuous function as the lower envelope of a family of convex functions. We discuss applications of conditions obtained to the examination of some tractable sufficient conditions for the global minimum and to the theory of inequalities.

引用

页码：101 / 123

页数：23

共 19 条

[1]

[Anonymous], 1982, Res. Notes in Math., V57, P43

[2] Global optimality conditions for quadratic optimization problems with binary constraints [J].

Beck, A ;

Teboulle, M .

SIAM JOURNAL ON OPTIMIZATION, 2000, 11 (01) :179-188

[3] Necessary and sufficient global optimality conditions for convex maximization revisited [J].

Dur, M ;

Horst, R ;

Locatelli, M .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1998, 217 (02) :637-649

[4] Conditions for global optimality 2 [J].

Hiriart-Urruty, JB .

JOURNAL OF GLOBAL OPTIMIZATION, 1998, 13 (04) :349-367

[5]

Hiriart-Urruty JB, 2001, J GLOBAL OPTIM, V21, P445

[6]

Hiriart-Urruty JB., 1996, J CONVEX ANAL, V3, P55

[7]

HIRIARTURRUTY JB, 1993, CONVEX ANAL MINIMNIZ, V2

[8]

Horst R., 1995, Handbook of Global Optimization: Nonconvex Optimization and Its Application

[9]

Pallaschke D., 1997, Foundations of Mathematical Optimization

[10] Global optimum shape design [J].

Pan, XC ;

Zheng, QA .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 1999, 37 (4-5) :151-162

← 1 2 →