Displaying similar documents to “Characterizations of error bounds for lower semicontinuous functions on metric spaces”

Metric subregularity for nonclosed convex multifunctions in normed spaces

Xi Yin Zheng, Kung Fu Ng (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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In terms of the normal cone and the coderivative, we provide some necessary and/or sufficient conditions of metric subregularity for (not necessarily closed) convex multifunctions in normed spaces. As applications, we present some error bound results for (not necessarily lower semicontinuous) convex functions on normed spaces. These results improve and extend some existing error bound results.

A Note on Coercivity of Lower Semicontinuous Functions and Nonsmooth Critical Point Theory

Corvellec, J. (1996)

Serdica Mathematical Journal

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The first motivation for this note is to obtain a general version of the following result: let E be a Banach space and f : E → R be a differentiable function, bounded below and satisfying the Palais-Smale condition; then, f is coercive, i.e., f(x) goes to infinity as ||x|| goes to infinity. In recent years, many variants and extensions of this result appeared, see [3], [5], [6], [9], [14], [18], [19] and the references therein. A general result of this type was given in [3, Theorem 5.1]...

Applications of the Fréchet subdifferential

Durea, M. (2003)

Serdica Mathematical Journal

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2000 Mathematics Subject Classification: 46A30, 54C60, 90C26. In this paper we prove two results of nonsmooth analysis involving the Fréchet subdifferential. One of these results provides a necessary optimality condition for an optimization problem which arise naturally from a class of wide studied problems. In the second result we establish a sufficient condition for the metric regularity of a set-valued map without continuity assumptions.

A regularization method for ill-posed bilevel optimization problems

Maitine Bergounioux, Mounir Haddou (2006)

RAIRO - Operations Research

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We present a regularization method to approach a solution of the pessimistic formulation of ill-posed bilevel problems. This allows to overcome the difficulty arising from the non uniqueness of the lower level problems solutions and responses. We prove existence of approximated solutions, give convergence result using Hoffman-like assumptions. We end with objective value error estimates.