Optimality Conditions in Nondifferentiable G-Invex Multiobjective Programming
Division of Mathematical Sciences, Pukyong National University, Busan 608-737, South Korea
Journal of Inequalities and Applications 2010, 2010:172059 doi:10.1155/2010/172059Published: 16 March 2010
We consider a class of nondifferentiable multiobjective programs with inequality and equality constraints in which each component of the objective function contains a term involving the support function of a compact convex set. We introduce G-Karush-Kuhn-Tucker conditions and G-Fritz John conditions for our nondifferentiable multiobjective programs. By using suitable G-invex functions, we establish G-Karush-Kuhn-Tucker necessary and sufficient optimality conditions, and G-Fritz John necessary and sufficient optimality conditions of our nondifferentiable multiobjective programs. Our optimality conditions generalize and improve the results in Antczak (2009) to the nondifferentiable case.