On G -invex multiobjective programming. Part II. Duality Article First Online: 12 April 2008 Received: 10 May 2007 Accepted: 08 March 2008 DOI :
10.1007/s10898-008-9298-6

Cite this article as: Antczak, T. J Glob Optim (2009) 43: 111. doi:10.1007/s10898-008-9298-6
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Abstract This paper represents the second part of a study concerning the so-called G -multiobjective 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 G -invex multiobjective programming. Part I. Optimality by T.Antczak. In this work, we use a generalization of convexity, namely G -invexity, 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 so-called G -Mond–Weir, G -Wolfe and G -mixed dual vector problems to the primal one are defined. Furthermore, various so-called G -duality theorems are proved between the considered differentiable multiobjective programming problem and its nonconvex vector G -dual 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) G -invex vector function with respect to η G -Karush–Kuhn–Tucker necessary optimality conditions G -Mond–Weir vector dual problems G -Wolfe vector dual problem G -mixed vector dual problem

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Authors and Affiliations 1. Faculty of Mathematics and Computer Science University of Łódź Lodz Poland