Error bounds for an inequality system

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dc.contributor.author Wu, Zili
dc.date.accessioned 2018-10-23T19:13:37Z
dc.date.available 2018-10-23T19:13:37Z
dc.date.copyright 2001 en_US
dc.date.issued 2018-10-23
dc.identifier.uri http://hdl.handle.net/1828/10174
dc.description.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. en_US
dc.language English eng
dc.language.iso en en_US
dc.rights Available to the World Wide Web en_US
dc.subject Inequalities (Mathematics) en_US
dc.subject Error analysis (Mathematics) en_US
dc.title Error bounds for an inequality system en_US
dc.type Thesis en_US
dc.contributor.supervisor Ye, Jane J.
dc.degree.department Department of Philosophy en_US
dc.degree.level Doctor of Philosophy Ph.D. en_US
dc.description.scholarlevel Graduate en_US

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