Existence of solutions and error bound for vector variational inequalities in Banach spaces. (2nd September 2018)

• Record Type: Journal Article
• Authors: Yao, Jen-Chih; Zheng, Xi Yin
• Is Part Of: Optimization. Volume 67:Number 9(2018)
• Page Start: 1333
• Page End: 1344
• Publication Date: 2018-09-02
• Subjects: Vector variational inequality -- fixed point -- gap function -- error bound; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2018.1429433
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract: Without monotonicity and convexity assumptions, we provide the existence results of solutions for weak vector variational inequalities and vector variational inequalities under some kinds of continuity assumptions. We give a gap function for a weak vector variational inequality and present a sufficient condition to guarantee that the vector variational inequality has error bound property with respect to such a gap function.