Results 91 to 100 of about 2,024 (222)
Topological Properties of the Approximate Subdifferential
, 1994 The approximate subdifferential introduced by Mordukhovich has attracted much attention in recent works on nonsmooth optimization. Potential advantages over other concepts of subdifferentiability might be related to its non-convexity.
René Henrion
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Extensions Of Subdifferential Calculus Rules in Banach Spaces
, 1996 This paper is devoted to extending formulas for the geometric approximate subdifferential and the Clarke subdifferential of extended-real-valued functions on Banach spaces.
A. Jourani, L. Thibault
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Abstract and Applied Analysis, 2014 We mainly present several equivalent characterizations of the strong metric subregularity of the Mordukhovich subdifferential for an extended-real-valued lower semicontinuous, prox-regular, and subdifferentially continuous function acting on an Asplund ...
J. J. Wang, W. Song
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About subdifferential calculus for abstract convex functions
, 2007 We introduce a stronger version of the strong globalization property of Rolewicz and examine the corresponding subdifferential calculus for abstract convex functions.
Sharikov, Evgenii
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Upper Semi-Continuity of Subdifferential Mappings
, 1980 Characterizations of the upper semi-continuity of the subdifferential mapping of a continuous convex function are given.
David A. Gregory
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Abstract and Applied Analysis, 2013 We obtain a new Taylor's formula in terms of the order subdifferential of a function from to . As its applications in optimization problems, we build order sufficient optimality conditions of this kind of functions and order necessary conditions ...
He Qinghai, Zhang Binbin
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Subdifferential characterization of probability functions under Gaussian distribution [PDF]
, 2018 © 2018, Springer-Verlag GmbH Germany, part of Springer Nature and Mathematical Optimization Society. Probability functions figure prominently in optimization problems of engineering. They may be nonsmooth even if all input data are smooth.
Henrion, René +5 more
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On generalized derivatives for C1,1 vector optimization problems
Journal of Applied Mathematics, 2003 We introduce generalized definitions of Peano and Riemann directional derivatives in order to obtain second-order optimality conditions for vector optimization problems involving C1,1 data.
Davide La Torre
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The directional subdifferential of the difference of two convex functions
We provide a criterion giving a formula for the directional (or contingent) subdifferential of the difference of two convex functions. We even extend it to the difference of two approximately starshaped functions.
Jean-Paul Penot
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Lipschitz functions with minimal Clarke subdifferential mappings
, 1996 In this paper we characterise, in terms of the upper Dini derivative, when the Clarke subdifferential mapping of a real-valued locally Lipschitz function is a minimal weak cusco.
Jonathan M. Borwein, Warren B. Moors
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