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)
DOI: https://doi.org/10.58250/Jnanabha.2021.51101
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.