Optimality Conditions and Duality for MultiobjectiveSemi-infinite Optimization Problems with SwitchingConstraints 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 (abbreviated as, (ACQ)) for (MSIPSC) in Hadamard manifold setting.Necessary criteria of weak Pareto efficiency for (MSIPSC) are established by employing (ACQ). Further, sufficient criteria of weak Pareto efficiency for (MSIPSC) are established by using geodesic quasiconvexity and pseudoconvexityassumptions. Subsequently, Mond-Weir type and Wolfe type dual modelsare formulated related to the primal problem (MSIPSC), and thereafter several duality results are established that relate (MSIPSC) and the correspondingdual models. Several interesting non trivial examples are furnished in the framework of well-known Hadamard manifolds, such as the set consistingof all symmetric positive definite matrices and the Poincaré half plane, toillustrate the importance of the results derived in this article. To the best ofour knowledge, this is the first time that optimality conditions and duality for (MSIPSC) have been studied in the setting of Hadamard manifolds Mathematics Subject Classification (2000) 90C34 · 90C46 · 90C48 · 90C29