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
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.