All ressources related to this research area.
Modern Convex Analysis
Some of my articles on Convex Analysis deal with: Calculus without qualification conditions, Steepest descent equations governed by subdifferentials of convex functions, etc
Related book(s)
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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
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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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C1,.-regularity and Lipschitz-like properties of subdifferential.
Author(s):Jourani, Thibault, Zagrodny
Related research area(s): Modern Convex Analysis, Variational Nonsmooth Analysis
Journal: Proceedings of London Mathematical Society
Reference: 105 (2012), 189--223.
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A note on subdifferentials of convex composite functionals
Related research area(s): Modern Convex Analysis
Journal: Archiv der Mathematik
Reference: 67 (1996), 239--252.
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A subdifferential characterization of Motzkin decomposable functions
Author(s):Martinez-Legaz, Thibault
Related research area(s): Modern Convex Analysis
Journal: Optimization
Reference: 68 (2019), 1279--1287.
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Characterization of lower semicontinuous convex functions
Author(s):Correa, Jofré, Thibault
Related research area(s): Modern Convex Analysis, Variational Nonsmooth Analysis
Journal: Proceedings of American Mathematical Society
Reference: 116 (1992), 67--72.
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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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Continuity of measurable convex and biconvex operators
Author(s):Thibault
Related research area(s): Modern Convex Analysis
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Convergence of subdifferentials of convexly composite functions
Author(s):Combari, Poliquin, Thibault
Related research area(s): Modern Convex Analysis, Variational Nonsmooth Analysis
Journal: Canadian Journal of Mathematics
Reference: 51 (1999), 250--265.
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Convex sweeping process in the framework of measure differential inclusions and evolution variational inequalities
Author(s):Adly, Haddad, Thibault
Related research area(s): Differential Inclusions, Modern Convex Analysis, Set-Valued Analysis
Journal: Mathematical Programming
Reference: 148 (2014), 5--48.
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D-representation of subdifferentials of directionally Lipschitz functions
Related research area(s): Modern Convex Analysis, Variational Nonsmooth Analysis
Journal: Proceedings of American Mathematical Society
Reference: 110 (1990), 117--123.
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Directional derivatives and almost everywhere differentiability of biconvex and concave-convex operators
Related research area(s): Modern Convex Analysis
Journal: Mathematica Scandinavica
Reference: 57 (1985), 215--224.
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Envelopes for sets and functions II: generalized polarity and conjugacy
Author(s):Cabot, Jourani, Thibault
Related research area(s): Modern Convex Analysis, Optimization
Journal: Linear and Nonlinear Analysis
Reference: 19 (2018), 1297--1318.
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Envelopes for sets and functions: regularization and generalized conjugacy
Author(s):Cabot, Jourani, Thibault
Related research area(s): Modern Convex Analysis, Variational Nonsmooth Analysis
Journal: Mathematika
Reference: 63 (2017), 383--432.
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Epiconvergence of convexly composite functions in Banach spaces
Related research area(s): Modern Convex Analysis, Variational Nonsmooth Analysis
Journal: SIAM Journal on Optimization
Reference: 13 (2003), 986--1003.
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Equicontinuity of families of convex and concave-convex operators
Related research area(s): Modern Convex Analysis
Journal: Canadian Journal of Mathematics
Reference: 36 (1984), 883--898.
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Familles équilipschitziennes d'applications convexes ou biconvexes vectorielles
Related research area(s): Modern Convex Analysis
Journal: Comptes Rendus de l'Académie des Sciences de Paris
Reference: 298 (1984), 83--85.
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Integrability of subdifferentials of certain bivariate functions
Related research area(s): Modern Convex Analysis, Variational Nonsmooth Analysis
Journal: Nonlinear Analysis
Reference: 54 (2003), 1251--1269.
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Integration of epsilon-Fenchel subdifferentials and maximal cyclic monotonicity
Related research area(s): Modern Convex Analysis
Journal: Journal of Global Optimization
Reference: 32 (2005), 83--91.
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Lipschitz continuity of V-subdifferentials of convex operators
Author(s):Thibault
Related research area(s): Modern Convex Analysis
Journal: Journal of Optimization Theory and Applications
Reference: 46 (1985), 205--213.
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On subdifferential calculus for convex functions defined on locally convex spaces
Author(s):Combari, Laghdir, Thibault
Related research area(s): Modern Convex Analysis
Journal: Annales des Sciences Mathématiques du Québec
Reference: 23 (1999), 23--36.
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On the graph convergence of epsilon-Fenchel subdifferentials of convex functions
Author(s):Combari, Marcellin, Thibault
Related research area(s): Modern Convex Analysis
Journal: Journal of Nonlinear and Convex Analysis
Reference: 4 (2003), 309--324.
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On the graph convergence of subdifferentials of convex functions
Related research area(s): Modern Convex Analysis
Journal: Proceedings of American Mathematical Society
Reference: 126 (1998), 2231--2240.
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Partially ball weakly inf-compact saddle functions
Related research area(s): Modern Convex Analysis
Journal: Mathematics of Operations research
Reference: 30 (2005), 404--419.
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Prox-regular sets and Legendre-Fenchel transform related to separation properties
Author(s):Adly, Nacry, Thibault
Related research area(s): Modern Convex Analysis, Variational Nonsmooth Analysis
Journal: Optimization
Reference: 71 (2022), 2097--2129.
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Sequential convex subdifferential calculus and sequential Lagrange multipliers
Author(s):Thibault
Related research area(s): Modern Convex Analysis
Journal: SIAM Journal on Control and Optimization
Reference: 35 (1997), 1434--1444.
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Sequential formulae for the normal cone to sublevel sets
Related research area(s): Modern Convex Analysis
Journal: Transactions of American Mathematical Society
Reference: 366 (2014), 6591--6628.
Download: article
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Sequential of integral sum of convex functions
Related research area(s): Modern Convex Analysis
Journal: Journal of Nonlinear and Convex Analysis
Reference: 9 (2008), 295--308.
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Sous-différentiels de fonctions convexes composites
Author(s):Combari, Laghdir, Thibault
Related research area(s): Modern Convex Analysis
Journal: Annales des Sciences Mathématiques du Québec
Reference: 18 (1994), 119--148.
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Subdifferential analysis of bivariate separately regular functions
Related research area(s): Modern Convex Analysis, Variational Nonsmooth Analysis
Journal: Journal of Mathematical Analysis and Applications
Reference: 148 (1990), 157--174.
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Subdifferential monotonicity as characterization of convex functions
Author(s):Correa, Jofré, Thibault
Related research area(s): Modern Convex Analysis, Variational Nonsmooth Analysis
Journal: Numerical Functional Analysis and Optimization
Reference: 15 (1994), 531--535.
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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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V-subdifferentials of convex operators
Author(s):Thibault
Related research area(s): Modern Convex Analysis
Journal: Journal of Mathematical Analysis and Applications
Reference: 115 (1986), 442--460.
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Variational convergence of composed convex functions
Related research area(s): Modern Convex Analysis, Optimization
Journal: Journal of Positivity
Reference: 9 (2005), 115--147.
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Various Lipschitz-like properties for functions and sets I: Directional derivative and tangential characterizations
Author(s):Correa, Gajardo, Thibault
Related research area(s): Modern Convex Analysis, Variational Nonsmooth Analysis
Journal: SIAM Journal on Optimization
Reference: 20 (2010), 1766--1785.
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Weak compactness of sublevel sets in complete locally convex spaces
Author(s):Perez-Aros, Thibault
Related research area(s): Functional analysis, Modern Convex Analysis
Journal: Journal of Convex Analysis
Reference: 26 (2019), 739--751.