Error bounds for convex constrained systems in Banach spaces
Wen Song (2007)
Control and Cybernetics
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Wen Song (2007)
Control and Cybernetics
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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.
Wu, Zili (2010)
Fixed Point Theory and Applications [electronic only]
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Ioffe, A., Lucchetti, R.E. (2005)
Abstract and Applied Analysis
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Goga, Georgiana (2005)
Analele Ştiinţifice ale Universităţii “Ovidius" Constanţa. Seria: Matematică
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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]...
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.
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.