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Vietnam Journal of Mathematics 40:2&3(2012)
231-253
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Gap Functions and Error Bounds for Variational
and Generalized Variational Inequalities
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Joydeep Dutta
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Department of Mathematics and Statistics, Indian
Institute of Technology,
Kanpur-208016,
India
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Dedicated to Professor
Phan Quoc Khanh on the occasion of his 65th birthday
Received May 02, 2012
Revised September 11,
2012
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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.
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2000 Mathematics
Subject Classification. 90C33.
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Keywords.
Variational inequalities, generalized variational inequalities, gap functions,
error bounds, strong monotonicity, strong convexity.
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Established
by Vietnam Academy of Science and Technology &
Vietnam Mathematical Society
Published by
Springer since January 2013
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