Gap functions for constrained vector variational inequalities with applications. (2nd December 2017)

• Record Type: Journal Article
• Authors: Xu, Y. D.; Zhang, P. P.
• Is Part Of: Optimization. Volume 66:Number 12(2017)
• Page Start: 2171
• Page End: 2191
• Publication Date: 2017-12-02
• Subjects: Constrained vector variational inequality -- gap function -- error bound -- continuity -- image space analysis; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2017.1359593
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract: In this paper, the image space analysis is applied to investigate scalar-valued gap functions and their applications for a (parametric)-constrained vector variational inequality. Firstly, using a non-linear regular weak separation function in image space, a gap function of a constrained vector variational inequality is obtained without any assumptions. Then, as an application of the gap function, two error bounds for the constrained vector variational inequality are derived by means of the gap function under some mild assumptions. Further, a parametric gap function of a parametric constrained vector variational inequality is presented. As an application of the parametric gap function, a sufficient condition for the continuity of the solution map of the parametric constrained vector variational inequality is established within the continuity and strict convexity of the parametric gap function. These assumptions do not include any information on the solution set of the parametric constrained vector variational inequality.