Wolfe duality and Mond-Weir duality via perturbations

被引：14

作者：

Bot, Radu Ioan ^{[1
]}

Grad, Sorin-Mihai ^{[1
]}

机构：

[1] Tech Univ Chemnitz, Fac Math, D-09107 Chemnitz, Germany

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2010年 / 73卷 / 02期

关键词：

Wolfe duality; Mond-Weir duality; Conjugate functions; Convex subdifferentials; Regularity conditions;

D O I：

10.1016/j.na.2010.03.026

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Considering a general optimization problem, we attach to it by means of perturbation theory two dual problems having in the constraints a subdifferential inclusion relation. When the primal problem and the perturbation function are particularized different new dual problems are obtained. In the special case of a constrained optimization problem, the classical Wolfe and Mond-Weir duals, respectively, follow as particularizations of the general duals by using the Lagrange perturbation. Examples to show the differences between the new duals are given and a gate towards other generalized convexities is opened. (C) 2010 Elsevier Ltd. All rights reserved.

引用

页码：374 / 384

页数：11

共 9 条

[1] Duality for almost convex optimization problems via the perturbation approach
Bot, Radu Ioan
Kassay, Gabor
Wanka, Gert
[J]. JOURNAL OF GLOBAL OPTIMIZATION, 2008, 42 (03) : 385 - 399
[2] Bot RI, 2006, LECT NOTES ECON MATH, V583, P101
[3] Bot RI., 2010, CONJUGATE DUALITY CO
[4] Crouzeix JP, 2010, J CONVEX ANAL, V17, P521
[5] DUALITY THEOREMS FOR CONVEX-PROGRAMMING WITHOUT CONSTRAINT QUALIFICATION
KANNIAPPAN, P
[J]. JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY SERIES A-PURE MATHEMATICS AND STATISTICS, 1984, 36 (APR): : 253 - 266
[6] Mond B., 1981, P NATO ADV STUDY I, P263
[7] SUBGRADIENT DUALITY THEOREM
SCHECHTER, M
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1977, 61 (03) : 850 - 855
[8] Wolfe P., 1961, Quart. Appl. Math., V19, P239
[9] Zalinescu C., 2002, Convex Analysis in General Vector Spaces

← 1 →