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On G-invex multiobjective programming. Part II. Duality

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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.

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  1. Faculty of Mathematics and Computer Science, University of Łódź, Banacha 22, 90-238, Lodz, Poland

    Tadeusz Antczak

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  1. Tadeusz Antczak
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Correspondence to Tadeusz Antczak.

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Antczak, T. On G-invex multiobjective programming. Part II. Duality. J Glob Optim 43, 111–140 (2009). https://doi.org/10.1007/s10898-008-9298-6

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  • DOI: https://doi.org/10.1007/s10898-008-9298-6

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