Search results for "Normal cone"

showing 6 items of 6 documents

Contribution to variational analysis : stability of tangent and normal cones and convexity of Chebyshev sets

2014

The aim of this thesis is to study the following three problems: 1) We are concerned with the behavior of normal cones and subdifferentials with respect to two types of convergence of sets and functions: Mosco and Attouch-Wets convergences. Our analysis is devoted to proximal, Fréchet, and Mordukhovich limiting normal cones and subdifferentials. The results obtained can be seen as extensions of Attouch theorem to the context of non-convex functions on locally uniformly convex Banach space. 2) For a given bornology β on a Banach space X we are interested in the validity of the following "lim inf" formula (…).Here Tβ(C; x) and Tc(C; x) denote the β-tangent cone and the Clarke tangent cone to …

Contingent coneCône tangent de BouligandSuite minimisanteFonctions sous-régulières cône normal (tangent) de ClarkeClarke tangent (normal) coneMetric projection[MATH.MATH-GM] Mathematics [math]/General Mathematics [math.GM]Chebyshev setMosco (Attouch-Wets) convergenceAsplund spaceCône normal proximalProjection metriqueEnsemble de ChebyshevConvergence au sens de Mosco (d'Attouch-Wets)Subsmooth sets (functions)BornologyBornologieMinimizing sequenceProximal normal coneFréchet (Mordukhovich limiting) subdifferentialEspace d'AsplundTrustworthinessSous-différentiel de Fréchet (de Mordukhovich)Ensembles sous-réguliers
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Invariant approximation results in cone metric spaces

2011

‎Some sufficient conditions for the existence of fixed point of mappings‎ ‎satisfying generalized weak contractive conditions is obtained‎. ‎A fixed‎ ‎point theorem for nonexpansive mappings is also obtained‎. ‎As an application‎, ‎some invariant approximation results are derived in cone metric spaces‎.

Control and OptimizationAlgebra and Number TheoryInjective metric spaceTangent coneMathematical analysis‎non normal cone‎54C60‎54H25‎‎orbitally continuous‎cone metric spacesIntrinsic metricConvex metric spaceFixed pointsMetric space‎46B40Dual cone and polar coneSettore MAT/05 - Analisi MatematicaMetric map‎invariant‎ ‎approximationInvariant (mathematics)Fixed points orbitally continuous invariant approximation cone metric spaces non normal cone.47H10AnalysisMathematics
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Prices and Pareto optima

2006

We provide necessary conditions for Pareto optimum in economies where tastes or technologies may be nonconvex, nonsmooth, and affected by externalities. Firms can pursue own objectives, much like the consumers. Infinite-dimensional commodity spaces are accommodated. Public goods and material balances are accounted for as special instances of linear restrictions.

Microeconomicsjel:C60first and second welfare theorem; weak and strong Pareto optimum; nonconvex tastes or technologies; public goods; externalities; local separation; subdifferentials; normal conesControl and OptimizationApplied Mathematicsjel:D60jel:D50EconomicsPareto principleManagement Science and Operations ResearchPublic goodCommodity (Marxism)ExternalityOptimization
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Regularization of perturbed state-dependent sweeping processes with nonregular sets

2018

International audience; In this paper, we prove the convergence strongly pointwisely (up to a subsequence) of Moreau-Yosida regularization of perturbed state-dependent sweeping process with nonregular (subsmooth and positively alpha-far) sets in separable Hilbert spaces. Some relevant consequences are indicated.

Positively alpha-far sets[MATH.MATH-GM]Mathematics [math]/General Mathematics [math.GM]MSC: 34A60 49J52 34G25 49J53Moreau-Yosida regularizationDifferential inclusions[MATH.MATH-GM] Mathematics [math]/General Mathematics [math.GM]Subsmooth setsSweeping processClarke normal cone
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Constrained differential inclusions with nonlocal initial conditions

2017

International audience; We show existence for the perturbed sweeping process with nonlocal initial conditions under very general hypotheses. Periodic, anti-periodic, mean value and multipoints conditions are included in this study. We give abstract results for differential inclusions with nonlocal initial conditions through bounding functions and tangential conditions. Some applications to differential complementarity systems and to vector hysteresis are given.

[ MATH.MATH-OC ] Mathematics [math]/Optimization and Control [math.OC]MSC: 34A60 49J52 34G25 49J53 34B10Periodic solutionsNonlocal Cauchy problemDifferential inclusions[MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC][MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC]Sweeping processesNormal coneBounding functions
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Differential inclusions involving normal cones of nonregular sets in Hilbert spaces

2017

This thesis is dedicated to the study of differential inclusions involving normal cones of nonregular sets in Hilbert spaces. In particular, we are interested in the sweeping process and its variants. The sweeping process is a constrained differential inclusion involving normal cones which appears naturally in several applications such as elastoplasticity, electrical circuits, hysteresis, crowd motion, etc.This work is divided conceptually in three parts: Study of positively alpha-far sets, existence results for differential inclusions involving normal cones and characterizations of Lyapunov pairs for the sweeping process. In the first part (Chapter 2), we investigate the class of positivel…

[ MATH.MATH-OC ] Mathematics [math]/Optimization and Control [math.OC]cône normalMoreau-Yosida regularizationcono normalmétodo de tipo Galerkinfonction distanceGalerkin-like methodMSC: 34A60 49J52 34G25 49J53 34B10 93D30subdiferencial de Clarkeprocessus de rafleInclusión diferencialensembles positivement alpha-far'sweeping processfonctions de Lyapunovsous-différentiel de Clarkeprocesos de arrastrefunción distanciaLyapunov functionsconjuntos positivamente alpha-farFunciones de Lyapunovméthode de type Galerkinrégularisation de Moreau-YosidaDifferential inclusions[MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC]Clarke subdifferentialregularización de Moreau-YosidaDistance functionInclusion différentielle[MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC]Normal conepositively alpha-far sets
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