Journal of Global Optimization

, Volume 43, Issue 1, pp 111-140

First online:

On G-invex multiobjective programming. Part II. Duality

  • Tadeusz AntczakAffiliated withFaculty of Mathematics and Computer Science, University of Łódź Email author 

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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.


(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