SET-VALUED OPTIMIZATION PROBLEMS WITH HIGHER-ORDER (α, β)-δ-CONE CONVEXITY
By
Koushik Das1,2
1Officer on Special Duty (OSD), Education Directorate, Department of Higher Education, Government of West Bengal, Bikash Bhawan, Kolkata, West Bengal, India - 700091 and 2Assistant Professor, Department of Mathematics, Government General Degree College Singur, Hooghly, West Bengal, India - 712409
Email: koushik@singurgovtcollege.org; koushikdas.maths@gmail.com
(Received: February 22, 2026; In format: February 28, 2026; Revised: March 26, 2026; Accepted: March 29, 2026)
DOI: https://doi.org/10.58250/jnanabha.2026.56111
Abstract
In this paper, we establish the higher-order sufficient Karush-Kuhn-Tucker (KKT) optimality conditions for set-valued optimization problems under the higher-order contingent epiderivative and higher-order (α, β)-δ-cone convexity assumptions. We also study the higher-order Mond-Weir (MW D) type of duality and establish the corresponding higher-order strong, weak and converse duality theorems in between the primal (P) and corresponding dual problem. An example is also developed to demonstrate that higher-order (α, β)-δ-cone convexity is more generalized than higherorder cone convexity.
2020 Mathematical Sciences Classification: 26B25; 49N15.
Keywords and Phrases: Convex cone; Set-valued map; Contingent epiderivative; Duality; Arcwisely connectedness.