Fritz-John Optimality and Duality for Non-convex Programs

In this paper we have obtained Fritz-John type necessary optimality criteria for non-linear programs under the hypotheses that the right differentials, at the optimal point, of the objective and the active constraint functions with respect to an arc are convex and the inactive constraint functions are continuous. A Mond- Weir type dual is associated and weak and strong duality results are established by assuming the functions involved to be locally P-connected. These results are further extended and necessary as well as sufficient optimality conditions are obtained for a weakly efficient solution of a multiobjective non-linear program. A proper weak minimum is defined and duality results are established by using this concept