Second-Order Optimality Conditions and Duality for Multiobjective Semi-Infinite Programming Problems on Hadamard Manifolds

Balendu Bhooshan Upadhyay (), Arnav Ghosh () and I. M. Stancu-Minasian
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Balendu Bhooshan Upadhyay: Department of Mathematics, Indian Institute of Technology Patna, India
Arnav Ghosh: Department of Mathematics, Indian Institute of Technology Patna, India
I. M. Stancu-Minasian: “Gheorghe Mihoc-Caius Iacob†Institute of Mathematical Statistics and Applied Mathematics of the Romanian Academy, Bucharest, Romania

Asia-Pacific Journal of Operational Research (APJOR), 2024, vol. 41, issue 02, 1-26

Abstract: This paper is devoted to the study of multiobjective semi-infinite programming problems on Hadamard manifolds. We consider a class of multiobjective semi-infinite programming problems (abbreviated as MSIP) on Hadamard manifolds. We use the concepts of second-order Karush–Kuhn–Tucker stationary point and second-order Karush–Kuhn–Tucker geodesic pseudoconvexity of the considered problem to derive necessary and sufficient second-order conditions of efficiency, weak efficiency and proper efficiency for MSIP along with certain generalized geodesic convexity assumptions. Moreover, we formulate the second-order Mond–Weir-type dual problem related to MSIP and deduce weak and strong duality theorems relating MSIP and the dual problem. The significance of our results is demonstrated with the help of non-trivial examples. To the best of our knowledge, this is the first time that second-order optimality conditions for MSIP have been studied in Hadamard manifold setting.

Keywords: Semi-infinite programming; multiobjective optimization; second-order optimality; duality; Hadamard manifolds (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1142/S0217595923500197

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