Journal of Global Optimization
, Volume 43, Issue 1, pp 111140
First online:
On Ginvex multiobjective programming. Part II. Duality
 Tadeusz AntczakAffiliated withFaculty of Mathematics and Computer Science, University of Łódź Email author
Rent the article at a discount
Rent now* Final gross prices may vary according to local VAT.
Get AccessAbstract
This paper represents the second part of a study concerning the socalled Gmultiobjective programming. A new approach to duality in differentiable vector optimization problems is presented. The techniques used are based on the results established in the paper: On Ginvex multiobjective programming. Part I. Optimality by T.Antczak. In this work, we use a generalization of convexity, namely Ginvexity, to prove new duality results for nonlinear differentiable multiobjective programming problems. For such vector optimization problems, a number of new vector duality problems is introduced. The socalled GMond–Weir, GWolfe and Gmixed dual vector problems to the primal one are defined. Furthermore, various socalled Gduality theorems are proved between the considered differentiable multiobjective programming problem and its nonconvex vector Gdual problems. Some previous duality results for differentiable multiobjective programming problems turn out to be special cases of the results described in the paper.
Keywords
(strictly) Ginvex vector function with respect to η GKarush–Kuhn–Tucker necessary optimality conditions GMond–Weir vector dual problems GWolfe vector dual problem Gmixed vector dual problem Title
 On Ginvex multiobjective programming. Part II. Duality
 Journal

Journal of Global Optimization
Volume 43, Issue 1 , pp 111140
 Cover Date
 200901
 DOI
 10.1007/s1089800892986
 Print ISSN
 09255001
 Online ISSN
 15732916
 Publisher
 Springer US
 Additional Links
 Topics
 Keywords

 (strictly) Ginvex vector function with respect to η
 GKarush–Kuhn–Tucker necessary optimality conditions
 GMond–Weir vector dual problems
 GWolfe vector dual problem
 Gmixed vector dual problem
 Industry Sectors
 Authors

 Tadeusz Antczak ^{(1)}
 Author Affiliations

 1. Faculty of Mathematics and Computer Science, University of Łódź, Banacha 22, 90238, Lodz, Poland