New concepts in nondifferentiable programming
J-B. Hiriart-Urruty (1979)
Mémoires de la Société Mathématique de France
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J-B. Hiriart-Urruty (1979)
Mémoires de la Société Mathématique de France
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María J. Cánovas, Abderrahim Hantoute, Marco A. López, Juan Parra (2009)
ESAIM: Control, Optimisation and Calculus of Variations
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We are concerned with the Lipschitz modulus of the optimal set mapping associated with canonically perturbed convex semi-infinite optimization problems. Specifically, the paper provides a lower and an upper bound for this modulus, both of them given exclusively in terms of the problem’s data. Moreover, the upper bound is shown to be the exact modulus when the number of constraints is finite. In the particular case of linear problems the upper bound (or exact modulus) adopts a notably...
Eva Matoušková (1993)
Acta Universitatis Carolinae. Mathematica et Physica
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Aleksander Ćwiszewski, Wojciech Kryszewski (2002)
Bollettino dell'Unione Matematica Italiana
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The paper deals with approximation of locally Lipschitz functionals. A concept of approximation, based on the idea of graph approximation of the generalized gradient, is discussed and the existence of such approximations for locally Lipschitz functionals, defined on open domains in , is proved. Subsequently, the procedure of a smooth normal approximation of the class of regular sets (containing e.g. convex and/or epi-Lipschitz sets) is presented.
Tomás Domínguez Benavides (1980)
Collectanea Mathematica
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Sven Heinrich (1986)
Czechoslovak Mathematical Journal
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Iryna Banakh, Taras Banakh, Anatolij Plichko, Anatoliy Prykarpatsky (2012)
Open Mathematics
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We find conditions for a smooth nonlinear map f: U → V between open subsets of Hilbert or Banach spaces to be locally convex in the sense that for some c and each positive ɛ < c the image f(B ɛ(x)) of each ɛ-ball B ɛ(x) ⊂ U is convex. We give a lower bound on c via the second order Lipschitz constant Lip2(f), the Lipschitz-open constant Lipo(f) of f, and the 2-convexity number conv2(X) of the Banach space X.