Optimality Conditions and Duality for Nonsmooth Multiobjective Semi-infinite Programming Problems on Hadamard Manifolds

In this article, we study a class of nonsmooth multiobjective semi-infinite programming problems defined on Hadamard manifolds [in short, (NMSIP)]. We present Abadie constraint qualification on Hadamard manifolds and employ it to derive necessary optimality conditions for (NMSIP). Moreover, by employing certain geodesic convexity restrictions on the objective functions and the constraints, we deduce sufficient optimality conditions for (NMSIP). Further, we formulate the Mond-Weir type and Wolfe-type dual models related to (NMSIP) and establish the weak, strong and strict converse duality results that relate the primal-dual pairs by employing geodesic convexity assumptions. We have furnished several non-trivial examples to justify the importance of the presented results. The results derived in this article generalize and extend several previously existing results in the literature.