Error bounds for an inequality system
Date
2018-10-23
Authors
Wu, Zili
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Abstract
For an inequality system, an error bound is an estimation for the distance from
any point to the solution set of the inequality. The Ekeland variational principle
(EVP) is an important tool in the study of error bounds. We prove that EVP is
equivalent to an error bound result and present several sufficient conditions for an
inequality system to have error bounds. In a metric space, a condition is similar to
that of Takahashi. In a Banach space we express conditions in terms of an abstract
subdifferential and the lower Dini derivative. We then discuss error bounds with
exponents by a relation between the lower Dini derivatives of a function and its
power function. For an l.s.c. convex function on a reflexive Banach space these
conditions turn out to be equivalent. Furthermore a global error bound closely
relates to the metric regularity.
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Keywords
Inequalities (Mathematics), Error analysis (Mathematics)