Abstract
In this paper, a generalization of convexity, namely G-invexity, is considered in the case of nonlinear multiobjective programming problems where the functions constituting vector optimization problems are differentiable. The modified Karush-Kuhn-Tucker necessary optimality conditions for a certain class of multiobjective programming problems are established. To prove this result, the Kuhn-Tucker constraint qualification and the definition of the Bouligand tangent cone for a set are used. The assumptions on (weak) Pareto optimal solutions are relaxed by means of vector-valued G-invex functions.
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Antczak, T. On G-invex multiobjective programming. Part I. Optimality. J Glob Optim 43, 97–109 (2009). https://doi.org/10.1007/s10898-008-9299-5
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DOI: https://doi.org/10.1007/s10898-008-9299-5