Optimality conditions and duality for multiobjective semi-infinite programming problems on Hadamard manifolds using generalized geodesic convexity

Abstract

This paper deals with multiobjective semi-infinite programming problems on Hadamard manifolds. We establish the sufficient optimality criteria of the considered problem under generalized geodesic convexity assumptions. Moreover, we formulate the Mond-Weir and Wolfe type dual problems and derive the weak, strong and strict converse duality theorems relating the primal and dual problems under generalized geodesic convexity assumptions. Suitable examples have also been given to illustrate the significance of these results. The results presented in this paper extend and generalize the corresponding results in the literature.

Optimality Conditions and Duality for MultiobjectiveSemi-infinite Optimization Problems with SwitchingConstraints on Hadamard Manifolds

“…On the other hand, the results derived this paper extend the corresponding results derived by Tung and Tam [51] to a wider class of programming problems, namely, (MSIPSC), and generalize them to a more general class of geodesic convex functions. Moreover, the results derived in this paper extend the results derived by Upadhyay et al [54] from smooth multiobjective (SIP) to (MSIPSC) in manifold setting. To the best of our knowledge, this is for the őrst time that optimality conditions and duality for (MSIPSC) have been studied in the setting of Hadamard manifolds.…”

“…In particular, the optimality conditions derived in this paper extend the corresponding conditions derived in [19] from Euclidean spaces to Hadamard manifolds. Further, the results derived this paper extend the corresponding results derived in [51,54] in manifold setting from smooth multiobjective (SIP) to a wider class of programming problems, namely, (MSIPSC).…”

“…Motivated by the works of [2,5,51,54], a class of (MSIPSC) in Hadamard manifold setting is investigated in the present article. We introduce (ACQ) for (MSIPSC) in the framework of Hadamard manifolds.…”

Optimality Conditions for Multiobjective Mathematical Programming Problems with Equilibrium Constraints on Hadamard Manifolds

“…which is a contradiction to (14). Hence, we can conclude that y ∈ D is a weakly efficient solution of (MMPEC).…”

“…The concepts of pseudoconvexity and quasiconvexity in a geodesic sense were introduced by Udrişte [6] in the Riemannian manifolds setting. Recently, many authors have generalized various other notions and concepts of optimization, from Euclidean spaces to Riemannian manifolds; see, for instance, [7][8][9][10][11][12][13][14][15][16][17][18] and the references cited therein.…”