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Journal of Convex Analysis 25 (2018), No. 4, 1121--1138
Copyright Heldermann Verlag 2018

The Dual Gap Function and Error Bounds for Strongly Monotone Variational Inequalities

Didier Aussel
Laboratoire PROMES, Université de Perpignan, 66100 Perpignan, France

Joydeep Dutta
Dept of Humanities and Social Sciences, Indian Institute of Technology, 208016 Kanpur, India

Andrew C. Xu
Massachusetts Institute of Technology, Cambridge, MA 02139, U.S.A.

In the literature of variational inequalities, there has been a lot of studies about the role of gap functions in the development of error bounds specially for the case where the variational inequality is described by a strongly monotone mapping. However the role of the dual gap function in devising error bounds, to the best of our knowledge, has not been thoroughly investigated. In this article we focus on the dual gap function for monotone variational inequalities. We highlight some properties of the dual gap function which are not shared by the other gap functions and also show how it can be used to develop error bounds for strongly monotone variational inequalities with convex and compact feasible sets.

Keywords: Variational inequalities, gap functions, error bounds, strongly monotone maps.

MSC: 90C33, 90C25

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