WSEAS Transactions on Mathematics
Print ISSN: 1109-2769, E-ISSN: 2224-2880
Volume 22, 2023
Duality for Multiobjective Programming Problems with Equilibrium Constraints on Hadamard Manifolds under Generalized Geodesic Convexity
Authors: , ,
Abstract: This article is devoted to the study of a class of multiobjective mathematical programming problems with equilibrium constraints on Hadamard manifolds (in short, (MPPEC)). We consider (MPPEC) as our primal problem and formulate two different kinds of dual models, namely, Wolfe and Mond-Weir type dual models related to (MPPEC). Further, we deduce the weak, strong as well as strict converse duality relations that relate (MPPEC) and the corresponding dual problems employing geodesic pseudoconvexity and geodesic quasiconvexity restrictions. Several suitable numerical examples are incorporated to demonstrate the significance of the deduced results. The results derived in this article generalize and extend several previously existing results in the literature.
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Keywords: Multiobjective optimization, Guignard constraint qualification, Generalized geodesic convexity, Duality, Hadamard manifolds
Pages: 259-270
DOI: 10.37394/23206.2023.22.31