On Approximately Star-Shaped Functions and Approximate Vector Variational Inequalities

On minty variational principle for nonsmooth vector optimization problems with approximate convexity

“…In this paper, we have studied a vector optimization problem involving locally Lipschitz approximately convex functions and gave a variant of the concept of approximate efficient solution as introduced in [14]. We have formulated approximate vector variational inequalities of Stampacchia and Minty type in terms of the Clarke subdifferentials and used these inequalities to find out an approximate efficient solution of the vector optimization problem.…”

“…The following concepts of efficient solutions (AES) is a variant of the concept of approximate efficient solution introduced in [14].…”

“…Vivek Laha laha.vivek333@gmail.com [5][6][7][8], the nonsmooth case [9][10][11][12] and the recent results [13][14][15] for motivations and references.…”

“…Later, White [26] proposed several concepts of approximate solutions for the vector optimization problems through scalarization. Recently, a concept of approximate efficient solution has been introduced by Mishra and Laha [14] and characterized using approximate vector variational inequalities of Stampacchia and Minty type under assumptions of approximately straight functions. The approximation procedures are of immense importance in optimization theory, because sometimes it is practically impossible or computationally very expensive to find out an exact solution.…”

On approximate starshapedness in multiobjective optimization

“…[2,3,6,12,16,17,23,[35][36][37]). We refer to the recent studies [9,13,19,[24][25][26][27][28] for motivation and references.…”