Necessary and sufficient second order optimality conditions for multiobjective problems with C1 data

被引：5

作者：

Santos, L. B. ^{[1
]}

Osuna-Gomez, R. ^{[2
]}

Hernandez-Jimenez, B. ^{[3
]}

Rojas-Medar, M. A. ^{[4
]}

机构：

[1] Univ Fed Parana, Ctr Politecn, Dpto Matemat, BR-81531980 Curitiba, Parana, Brazil

[2] Univ Seville, Fac Matemat, Dept Estat & Invest Operat, E-41012 Seville, Spain

[3] Univ Pablo de Olavide, Area Estat & Invest Operat, Dept Econ Metodos Cuantitat & Ha Econ, Seville 41013, Spain

[4] Univ Bio Bio, Fac Ciencias, Dpto Ciencias Basicas, Grp Matemat Aplicada, Chillan, Chile

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2013年 / 85卷

关键词：

Multiple objective programming; Generalized convexity; Optimality conditions; GENERALIZED CONVEXITY;

D O I：

10.1016/j.na.2013.02.020

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we obtain necessary and sufficient second order optimality conditions for multiobjective problems using second order directional derivatives. We propose the notion of second order KT-pseudoinvex problems and we prove that this class of problems has the following property: a problem is second order KT-pseudoinvex if and only if all its points that satisfy the second order necessary optimality condition are weakly efficient. Also we obtain second order sufficient conditions for efficiency. (C) 2013 Elsevier Ltd. All rights reserved.

引用

页码：192 / 203

页数：12

共 13 条

[1] Second-order optimality conditions in multiobjective optimization problems [J].

Aghezzaf, B ;

Hachimi, M .

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 1999, 102 (01) :37-50

[2] Pseudoinvexity, optimality conditions and efficiency in multiobjective problems; duality [J].

Arana-Jimenez, A. ;

Rufian-Lizana, A. ;

Osuna-Gomez, R. ;

Ruiz-Garzon, G. .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2008, 68 (01) :24-34

[3]

BENTAL A, 1982, MATH PROGRAM STUD, V19, P39, DOI 10.1007/BFb0120982

[4] Second order optimality conditions for differentiable multiobjective problems [J].

Bigi, G ;

Castellani, M .

RAIRO-RECHERCHE OPERATIONNELLE-OPERATIONS RESEARCH, 2000, 34 (04) :411-426

[5]

Chankong V., 2008, Multiobjective Decision Making Theory and Methodology

[6] Second-order optimality conditions for problems with C1 data [J].

Ginchev, Ivan ;

Ivanov, Vsevolod I. .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2008, 340 (01) :646-657

[7] ON SUFFICIENCY OF THE KUHN-TUCKER CONDITIONS [J].

HANSON, MA .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1981, 80 (02) :545-550

[8]

Ivanov V.I., 2010, J GLOBAL OPTIM, DOI DOI 10.1007/S10898-9610

[9] 2ND-ORDER NECESSARY CONDITIONS OF THE KUHN-TUCKER TYPE UNDER NEW CONSTRAINT QUALIFICATIONS [J].

KAWASAKI, H .

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 1988, 57 (02) :253-264

[10] THE ESSENCE OF INVEXITY [J].

MARTIN, DH .

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 1985, 47 (01) :65-76

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