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Vietnam Journal of Mathematics 40:2&3(2012) 231-253

 

Gap Functions and Error Bounds for Variational

and Generalized Variational Inequalities

Joydeep Dutta

Department of Mathematics and Statistics, Indian Institute of Technology,

Kanpur-208016, India

Dedicated to Professor Phan Quoc Khanh on the occasion of his 65th birthday

Received May 02, 2012

Revised September 11, 2012

Abstract. It is well known that gap functions play a major role in developing error bounds for strongly monotone and affine monotone variational inequalities. However the error bound would be important from the point of view of computation if the gap function values diminish on sequences of points which converge to a solution of the variational inequality. A gap function exhibiting such behavior is termed as a well-behaved gap function. In this article we would like to study some important gap functions for both variational inequalities with single-valued maps and set-valued maps and see what additional conditions one must impose on them so that they are well behaved.

2000 Mathematics Subject Classification. 90C33.

Keywords. Variational inequalities, generalized variational inequalities, gap functions, error bounds, strong monotonicity, strong convexity.

 

 

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