All ressources related to this research area.
Geometry of Banach spaces
Related book(s)
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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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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.
cover
Related article(s)
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Characterizations of prox-regular sets in uniformly convex Banach spaces
Author(s):Bernard, Thibault, Zlateva
Related research area(s): Geometry of Banach spaces, Modern Convex Analysis, Variational Nonsmooth Analysis
Journal: Journal of Convex Analysis
Reference: 13 (2006), 525--559.
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Prox-regular sets and epigraphs in uniformly convex Banach spaces: various regularities and properties
Author(s):Bernard, Thibault, Zlateva
Related research area(s): Functional analysis, Geometry of Banach spaces, Variational Nonsmooth Analysis
Journal: Transactions of American Mathematical Society
Reference: 363 (2011), 2211--2247.
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The attainment set of the phi-envelope and genericity properties
Author(s):Cabot, Jourani, Thibault, Zagrodny
Related research area(s): Geometry of Banach spaces, Modern Convex Analysis, Variational Nonsmooth Analysis
Journal: Mathematica Scandinavica
Reference: 124 (2019), 203--246.
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The NSLUC property and Klee envelope
Author(s):Jourani, Thibault, Zagrodny
Related research area(s): Functional analysis, Geometry of Banach spaces, Variational Nonsmooth Analysis
Journal: Mathematische Annalen
Reference: 365 (2016), 923--967.