Efficiency conditions and duality for multiobjective semi-infinite programming problems on Hadamard manifolds

Abstract

This paper is devoted to the study of a class of multiobjective semi-infinite programming problems on Hadamard manifolds (in short, (MOSIP-HM)). We derive some alternative theorems analogous to Tucker’s theorem, Tucker’s first and second existence theorem, and Motzkin’s theorem of alternative in the framework of Hadamard manifolds. We employ Motzkin’s theorem of alternative to establish necessary and sufficient conditions that characterize KKT pseudoconvex functions using strong KKT vector critical points and efficient solutions of (MOSIP-HM). Moreover, we formulate the Mond-Weir and Wolfe-type dual problems related to (MOSIP-HM) and derive the weak and converse duality theorems relating (MOSIP-HM) and the dual problems. Several non-trivial numerical examples are provided to illustrate the significance of the derived results. The results deduced in the paper extend and generalize several notable works existing in the literature.