Jñānābha‎, Vol. 51 (1) (2021), (1-11)

PARAMETRIC SET-VALUED OPTIMIZATION PROBLEMS UNDER GENERALIZED CONE CONVEXITY


By

¹Koushik Das1 and Chandal Nahak²

¹Department of Mathematics, Taki Government College, Taki - 743429, West Bengal, India

²Department of Mathematics, Indian Institute of Technology Kharagpur, Kharagpur - 721302, West Bengal, India

Email:koushikdas.maths@gmail.com; cnahak@maths.iitkgp.ac.in

(Received : February 11, 2020; Revised: February 19, 2021)

Abstract

In this paper, we establish sufficient Karush-Kuhn-Tucker (KKT) conditions for a parametric set-valued optimization problem under contingent epiderivative and generalized cone convexity assumptions. We also study duality results of Mond-Weir, Wolfe, and mixed types for weak solutions of a pair of set-valued optimization problems.


2010 Mathematics Subject Classifications: 26B25; 49N15.

Keywords and phrases: Convex Cone; Set-Valued Map; Contingent Epiderivative; Duality.



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