Vector variational inequality with pseudoconvexity on Hadamard manifolds. (1st December 2016)

• Record Type: Journal Article
• Authors: Chen, Sheng-lan; Fang, Chang-jie
• Is Part Of: Optimization. Volume 65:Number 12(2016)
• Page Start: 2067
• Page End: 2080
• Publication Date: 2016-12-01
• Subjects: Hadamard manifold -- pseudoconvex functions -- pseudomonotone vector fields -- Clarke subdifferential -- vector variational inequality -- vector optimization problem; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2016.1235161
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract : In this paper, we give some properties for nondifferentiable pseudoconvex functions on Hadamard manifolds, and discuss the connections between pseudoconvex functions and pseudomonotone vector fields. Moreover, we study Minty and Stampacchia vector variational inequalities, which are formulated in terms of Clarke subdifferential for nonsmooth functions. Some relations between the vector variational inequalities and nonsmooth vector optimization problems are established under pseudoconvexity or pseudomonotonicity. The results presented in this paper extend some corresponding known results given in the literatures.