Vector variational-like inequalities with generalized bifunctions defined on nonconvex sets
type: Item
instance of: scholarly article
title: Vector variational-like inequalities with generalized bifunctions defined on nonconvex sets
zbMATH Open document ID: 1182.47046
author: Sy-Ming Guu
author: Jun Li
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2009-07-24T00:00:00Z
review text: In this paper, the nonemptiness and compactness of solution sets for Stampacchia vector variational-like inequalities (for short, SVVLIs) and Minty vector variational-like inequalities (for short, MVVLIs) with generalized bifunctions defined on nonconvex sets are investigated by introducing the concepts of generalized weak cone-pseudomonotonicity and generalized (proper) cone-suboddness. The equivalent relations between a solution of SVVLIs and MVVLIs, and a generalized weakly efficient solution of vector optimization problems are established under the assumptions of generalized pseudoconvexity and generalized invexity in the sense of the Clarke generalized directional derivative.
Mathematics Subject Classification ID: 47J20
Mathematics Subject Classification ID: 90C29
zbMATH DE Number: 5586820
zbMATH Keywords: vector variational-like inequality
zbMATH Keywords: vector optimisation problem
zbMATH Keywords: generalised weak cone-pseudomonotonicity
zbMATH Keywords: generalised pseudoconvexity
zbMATH Keywords: generalised invexity
reviewed by: Zhang Xian
MaRDI profile type: Publication
full work available at URL: j.na.2009.01.137
OpenAlex ID: W2048195374
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DOI: 10.1016/J.NA.2009.01.137
description: scientific article; zbMATH DE number 5586820