OPTIMALITY CONDITIONS FOR (G, α) INVEX MULTIOBJECTIVE PROGRAMMING - Liu, X.; Yuan, D.; Yang, S.; Lai, G. (Journal of Nonlinear Analysis and Optimization: Theory & Applications (JNAO), 2011)
In this paper, a generalization of convexity, namely $(G, α)$-invexity, is considered in the case of nonlinear multiobjective programming problems where the functions constituting vector optimization problems are differentiable. Two auxiliary programming problems are constructed to present the modified KuhnTucker necessary optimality conditions for (CVP). With the help of auxiliary programming problems (GCVP), the relation between (CVP) and (GCVP) is discussed; while with the help of ('GP), a new KuhnTucker necessary condition for (CVP) is presented. Furthermore, the sufficiency of the introduced G KarushKuhnTucker(GKuhnTucker) necessary optimality conditions, for nonconvex multiobjective programming problem involving $(G, α)$-invex functions, is proved.