SET-VALUED OPTIMIZATION PROBLEMS WITH (p, r)-ρ -CONE ARCWISE CONNECTEDNESS
By
Koushik Das
Department of Mathematics, Taki Government College, Taki - 743429, West Bengal, India
Email:koushikdas.maths@gmail.com
(Received : November 01, 2021: Revised : December 24, 2021)
DOI: https://doi.org/10.58250/Jnanabha.2021.51232
Abstract
In this paper, we introduce a new type of generalized arcwise connectedness, namely (p,r)-ρ-cone arcwise connectedness, for set-valued optimization problems. We establish the sufficient Karush-Kuhn-Tucker (KKT) optimality conditions under contingent epiderivative and (p,r)-ρ-cone arcwise connectedness assumptions. Further, we study Mond-Weir (MWD), Wolfe (WD), and mixed (MD) types duality models and prove the corresponding weak, strong, and converse duality theorems between the primal (P) and the corresponding dual problems under (p,r)-ρ-cone arcwise connectedness assumption. We also construct an example to ensure that (p,r)-ρ-cone arcwise connectedness is more general than cone arcwise connectedness.
2020 Mathematical Sciences Classification: 26B25; 49N15.
Keywords and Phrases: Convex Cone; Set-Valued Map; Contingent Epiderivative; Arcwise Connectedness; Duality.