You can find here the books whose I was co-author and which are devoted to the development of variational and convex analysis.
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Unilateral Variational Analysis in Banach Spaces. Part II: Special Classes of Functions and Sets
Authors: Thibault
Editor: World Scientific
Publication date: 2023
Related research areas: Functional analysis, Geometry of Banach spaces, Modern Convex Analysis, Variational Nonsmooth Analysis
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.
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Unilateral Variational Analysis in Banach Spaces. Part I: General Theory
Authors: Thibault
Editor: World Scientific
Publication date: 2023
Related research areas: Functional analysis, Geometry of Banach spaces, Modern Convex Analysis, Variational Nonsmooth Analysis
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.
cover
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Prox-Regular Sets and Applications
Editor: International Press
Publication date: 2010
Related research areas: Modern Convex Analysis, Set-Valued Analysis, Variational Nonsmooth Analysis
The above title corresponds to a chapter, pages 99-182, of ''Handbook of Nonconvex Analysis and Applications'' Int. Press, Somerville, MA, 2010, Editor