Optimality conditions and duality for multiobjective semi-infinite optimization problems with switching constraints on Hadamard manifolds

Abstract

This paper deals with a certain class of multiobjective semi-infinite programming problems with switching constraints (in short, MSIPSC) in the framework of Hadamard manifolds. We introduce Abadie constraint qualification (in short, ACQ) for MSIPSC in the Hadamard manifold setting. Necessary criteria of weak Pareto efficiency for MSIPSC are derived by employing ACQ. Further, sufficient criteria of weak Pareto efficiency for MSIPSC are deduced by using geodesic quasiconvexity and pseudoconvexity assumptions. Subsequently, Mond–Weir type and Wolfe type dual models are formulated related to the primal problem MSIPSC, and thereafter, several duality results are established that relate MSIPSC and the corresponding dual models. Several non-trivial examples are furnished in the framework of well-known Hadamard manifolds, such as the set consisting of all symmetric positive definite matrices and the Poincaré half plane, to illustrate the importance of the results derived in this article. To the best of our knowledge, this is the first time that optimality conditions and duality results for MSIPSC have been studied in the setting of Hadamard manifolds.