Nonlinear Separation Approach to Inverse Variational Inequalities in Real Linear Spaces

Elisabeth Köbis (), Markus A. Köbis () and Xiaolong Qin ()
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Elisabeth Köbis: Martin Luther University Halle-Wittenberg
Markus A. Köbis: Free University Berlin
Xiaolong Qin: College of Mathematics and Computer Science, Zhejiang Normal University

Journal of Optimization Theory and Applications, 2019, vol. 183, issue 1, No 6, 105-121

Abstract: Abstract In this paper, we employ the image space analysis to study constrained inverse variational inequalities by means of a nonlinear separation approach. We introduce such a nonlinear functional, which is based on the known Gerstewitz functional, and show its property as a weak separation function and a regular weak separation function under different parameter sets. In contrast to known results, we do not assume any topology on the considered spaces. Then, an alternative theorem is established, which leads directly to a sufficient and necessary optimality condition of the constrained inverse variational inequality. Finally, a gap function and an error bound are obtained for the constrained inverse variational inequality.

Keywords: Inverse variational inequalities; Nonlinear separation; Image space analysis; Nonlinear scalarizing functional; Algebraic interior; Vector closure; 90C26; 90C29; 90C48 (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1007/s10957-019-01543-6

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