When is a Gap Function Good for Error Bounds?
نویسنده
چکیده
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 diminishes on sequence 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 consider 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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