On minty variational principle for quasidifferentiable vector optimization problems. (4th March 2023)

• Record Type: Journal Article
• Authors: Singh, Harsh Narayan; Laha, Vivek
• Is Part Of: Optimization methods and software. Volume 38:Number 2(2023)
• Page Start: 243
• Page End: 261
• Publication Date: 2023-03-04
• Subjects: Vector optimization -- quasidifferentiability -- variational inequalities -- generalized convexity -- nonsmooth analysis -- nonconvex analysis -- mean value theorem; 90C26 -- 49J40 -- 90C29 -- 49J52 -- 58E17; Mathematical optimization -- Periodicals; Algorithms -- Periodicals; 519.7
• DOI: 10.1080/10556788.2022.2119235
• Languages: English
• ISSNs: 1055-6788

Abstract

Abstract : This paper deals with quasidifferentiable vector optimization problems involving invex functions wrt convex compact sets. We present vector variational-like inequalities of Minty type and of Stampacchia type in terms of quasidifferentials denoted by (QMVVLI) and (QSVVLI), respectively. By utilizing these variational inequalities, we infer vital and adequate optimality conditions for an efficient solution of the quasidifferentiable vector optimization problem involving invex functions wrt convex compact sets. We also establish various results for the solutions of the corresponding weak versions of the vector variational-like inequalities in terms of quasidifferentials.