Optimality conditions and duality for multiobjective semi-infinite programming problems on Hadamard manifolds using generalized geodesic convexity

Abstract

This paper deals with multiobjective semi-infinite programming problems on Hadamard manifolds. We establish the sufficient optimality criteria of the considered problem under generalized geodesic convexity assumptions. Moreover, we formulate the Mond-Weir and Wolfe type dual problems and derive the weak, strong and strict converse duality theorems relating the primal and dual problems under generalized geodesic convexity assumptions. Suitable examples have also been given to illustrate the significance of these results. The results presented in this paper extend and generalize the corresponding results in the literature.