https://thibault.xyz Lionel Thibault Feed en-us Symphony (build 2.3.3) https://thibault.xyzprox-regular-sets-and-applications/ 02 Jun 2023 11:12 https://thibault.xyz2023-06-02T11:12:01+02:00 The above title corresponds to a chapter, pages 99-182, of ''Handbook of Nonconvex Analysis and Applications'' Int. Press, Somerville, MA, 2010, Editor https://thibault.xyzunilateral-variational-analysis-in-banach-spaces-part-ii-special-classes-of-functions-and-sets/ 02 Jun 2023 11:02 https://thibault.xyz2023-06-02T11:02:55+02:00 The monograph provides a detailed and comprehensive presentation of the rich and beautiful theory of unilateral variational analysis in infinite dimensions. It is divided into two volumes named Part I and Part II. Starting with the convergence of sets and the semilimits and semicontinuities of multimappings, the first volume develops the theories of tangent cones, of subdifferentials, of convexity and duality in locally convex spaces, of extended mean value inequalities in absence of differentiability, of metric regularity, of constrained optimization problems. The second volume is devoted to special classes of non-smooth functions and sets. It expands the theory of subsmooth functions and sets, of semiconvex functions and multimappings, of primal lower regular functions, of singularities of non-smooth mappings, of prox-regular functions and sets in general spaces, of differentiability of projection mapping and others for prox-regular sets. Both volumes I and II contain, for each chapter, extensive comments covering related developments and historical comments. Connected area fields of the material are: optimization, optimal control, variational inequalities, differential inclusions, mechanics, economics. The book is intended for PhD students, researchers, and practitioners using unilateral variational analysis tools. https://thibault.xyzunilateral-variational-analysis-in-banach-spaces-part-i-general-theory/ 02 Jun 2023 11:02 https://thibault.xyz2023-06-02T11:02:34+02:00 The monograph provides a detailed and comprehensive presentation of the rich and beautiful theory of unilateral variational analysis in infinite dimensions. It is divided into two volumes named Part I and Part II. Starting with the convergence of sets and the semilimits and semicontinuities of multimappings, the first volume develops the theories of tangent cones, of subdifferentials, of convexity and duality in locally convex spaces, of extended mean value inequalities in absence of differentiability, of metric regularity, of constrained optimization problems. The second volume is devoted to special classes of non-smooth functions and sets. It expands the theory of subsmooth functions and sets, of semiconvex functions and multimappings, of primal lower regular functions, of singularities of non-smooth mappings, of prox-regular functions and sets in general spaces, of differentiability of projection mapping and others for prox-regular sets. Both volumes I and II contain, for each chapter, extensive comments covering related developments and historical comments. Connected area fields of the material are: optimization, optimal control, variational inequalities, differential inclusions, mechanics, economics. The book is intended for PhD students, researchers, and practitioners using unilateral variational analysis tools. https://thibault.xyzcours-danalyse-fonctionnelle/ 21 Feb 2015 23:54 https://thibault.xyz2015-02-21T23:54:37+01:00 Ce polycopié présente de façon détaillée les premiers éléments d'Analyse Fonctionnelle. https://thibault.xyzlipschitz-perturbation-of-bv-sweeping-process/ 28 Sep 2013 04:23 https://thibault.xyz2013-09-28T04:23:02+02:00 <p>Talk presented in ''Journees annuelles: Mathematiques de l'Optimisation et Applications, Paris june 2013"<br></p> https://thibault.xyzcharacterizations-of-prox-regular-sets-in-uniformly-convex-banach-spaces/ NaN https://thibault.xyz https://thibault.xyzsubdifferential-determination-of-essentially-directionally-smooth-functions-in-banach-space/ NaN https://thibault.xyz https://thibault.xyzprox-regular-sets-and-epigraphs-in-uniformly-convex-banach-spaces-various-regularities-and-properties/ NaN https://thibault.xyz