All ressources related to this research area.
Variational Nonsmooth Analysis
Some of my research papers on Nonsmooth Variational Analysis develop various basic properties of prox-regular sets and functions, subsmooth sets, primal lower regular functions,...
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 general metric regularity in Asplund spaces
Author(s):Amahroq, Jourani, Thibault
Related research area(s): Variational Nonsmooth Analysis
Journal: Numerical Functional Analysis and Optimization
Reference: 19 (1998), 215--226.
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A note on Fréchet and approximate subdifferentials of composite functions
Related research area(s): Variational Nonsmooth Analysis
Journal: Bulletin of Australian Mathematical Society
Reference: 49 (1994), 111--115.
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A note on the Zagrodny mean value theorem
Author(s):Thibault
Related research area(s): Variational Nonsmooth Analysis
Journal: Optimization
Reference: 35 (1995), 127--130.
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Approximate and metric regularity in mathematical programming in Banach space
Related research area(s): Optimization, Variational Nonsmooth Analysis
Journal: Mathematics of Operations research
Reference: 18 (1993), 390--401.
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BV prox-regular sweeping process with bounded truncation
Related research area(s): Differential Inclusions, Variational Nonsmooth Analysis
Journal: Optimization
Reference: 69 (2020), 1391--1437.
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Calcul sous-différentiel et calcul des variations en dimension infinie
Author(s):Thibault
Related research area(s): Optimal Control , Variational Nonsmooth Analysis
Journal: Bulletin de la Société Mathématique de France
Reference: 60 (1979), 161--175.
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Chain rules for coderivatives of multivalued mappings in Banach spaces
Related research area(s): Set-Valued Analysis, Variational Nonsmooth Analysis
Journal: Proceedings of American Mathematical Society
Reference: 126 (1998), 1479--1485.
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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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Coderivative of multivalued mappings, locally compact cones and metric regularity
Related research area(s): Variational Nonsmooth Analysis
Journal: Nonlinear Analysis
Reference: 35 (1999), 925--945.
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Conditions nécessaires pour des problèmes de contrôle optimal définis par des fonctions compactement lipschitziennes
Author(s):Thibault
Related research area(s): Variational Nonsmooth Analysis
Journal: Comptes Rendus de l'Académie des Sciences de Paris
Reference: 288 (1979), 133--136.
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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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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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Differential properties of the Moreau envelope
Author(s):Jourani, Thibault, Zagrodny
Related research area(s): Variational Nonsmooth Analysis
Journal: Journal of Functional Analysis
Reference: 266 (2014), 1185--1237.
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Directionally pseudo-Lipschitz set-valued mappings
Related research area(s): Variational Nonsmooth Analysis
Journal: Journal of Mathematical Analysis and Applications
Reference: 266 (2002), 269--287.
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Discontinuous sweeping process with prox-regular sets
Author(s):Adly, Nacry, Thibault
Related research area(s): Variational Nonsmooth Analysis
Journal: ESAIM Control Optim. Calc. Var.
Reference: 23 (2017), 1293--1329.
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Distance function associated to a prox-regular set
Related research area(s): Variational Nonsmooth Analysis
Journal: Set-Valued and Variational Analysis
Reference: 30 (2022), 731--750.
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Enlarged inclusions of subdifferentials
Related research area(s): Set-Valued Analysis, Variational Nonsmooth Analysis
Journal: Canadian Mathematical Bulletin
Reference: 48 (2005), 283--301.
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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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Epi-différentiels de fonctions vectorielles
Author(s):Thibault
Related research area(s): Variational Nonsmooth Analysis
Journal: Comptes Rendus de l'Académie des Sciences de Paris
Reference: 290 (1980), 87--90.
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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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Espérances conditionnelles d'intégrandes lipschitziens et d'intégrandes semi-continus inférieurement
Author(s):Thibault
Related research area(s): Variational Nonsmooth Analysis
Journal: Comptes Rendus de l'Académie des Sciences de Paris
Reference: 291 (1980), 551--554.
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Evolution differential inclusions associated to primla lower regular functions
Related research area(s): Differential Inclusions, Set-Valued Analysis, Variational Nonsmooth Analysis
Journal: Journal of Nonlinear and Convex Analysis
Reference: 20 (2019), 1949--1979.
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Evolution problems associated with primal lower nice functions
Related research area(s): Set-Valued Analysis, Variational Nonsmooth Analysis
Journal: Journal of Convex Analysis
Reference: 13 (2006), 385--421.
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Existence et caractérisation de différentielles généralisées d'applications localement lipschiziennes d'un espace de Banach séparable dans un espace de Banach réflexif
Author(s):Hiriart-Urruty, Thibault
Related research area(s): Variational Nonsmooth Analysis
Journal: Comptes Rendus de l'Académie des Sciences de Paris
Reference: 290 (1980), 1091--1094.
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Extensions of subdifferential calculus rules in Banach spaces
Related research area(s): Variational Nonsmooth Analysis
Journal: Canadian Journal of Mathematics
Reference: 48 (1996), 183--201.
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Fonctions compactement lipschitziennes et programmation mathématique
Author(s):Thibault
Related research area(s): Variational Nonsmooth Analysis
Journal: Comptes Rendus de l'Académie des Sciences de Paris
Reference: 287 (1978), 213--216.
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Inclusion and integration of subdifferentials
Related research area(s): Variational Nonsmooth Analysis
Journal: Journal of Nonlinear and Convex Analysis
Reference: 3 (2002), 411--434.
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Infimal convolution and optimal time control problem I: Frechet and proximal subdifferential
Related research area(s): Optimization, Variational Nonsmooth Analysis
Journal: Set-Valued and Variational Analysis
Reference: 26 (2018), 581--606.
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Infimal convolution and optimal time control problem II: limiting subdifferential
Related research area(s): Optimization, Variational Nonsmooth Analysis
Journal: Set-Valued and Variational Analysis
Reference: 25 (2017), 517--542.
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Infimal convolution and optimal time control problem III: minimal time projection set
Related research area(s): Optimization, Variational Nonsmooth Analysis
Journal: SIAM Journal on Optimization
Reference: 28 (2018), 30--44.
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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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Integrability of subdifferentials of directionally Lipschitz functions
Related research area(s): Variational Nonsmooth Analysis
Journal: Proceedings of American Mathematical Society
Reference: 133 (2005), 2939--2948.
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Integration of primal lower nice functions in Hilbert space
Author(s):Bernard, Thibault, Zagrodny
Related research area(s): Variational Nonsmooth Analysis
Journal: Journal of Optimization Theory and Applications
Reference: 124 (2005), 561--579.
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Integration of subdifferentials oof lower semicontinuous functions on Banach spaces
Related research area(s): Variational Nonsmooth Analysis
Journal: Journal of Mathematical Analysis and Applications
Reference: 189 (1995), 33--58.
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Local differentiability of distance functions
Author(s):Poliquin, Rockafellar, Thibault
Related research area(s): Variational Nonsmooth Analysis
Journal: Transactions of American Mathematical Society
Reference: 352 (2000), 5231--5249.
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Metric projection and compatibly parameterized families of prox-regular sets in Hilbert space
Related research area(s): Variational Nonsmooth Analysis
Journal: Nonlinear Analysis
Reference: 75 (2012), 1547--1562.
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Metric regularity and subdifferential calculus in Banach space
Related research area(s): Variational Nonsmooth Analysis
Journal: Set-Valued Analysis
Reference: 3 (1995), 87--100.
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Metric regularity for strongly compactly Lipschitzian mappings
Related research area(s): Optimization, Variational Nonsmooth Analysis
Journal: Nonlinear Analysis
Reference: 24 (1995), 229--240.
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Moreau envelopes of s-lower regular functions
Related research area(s): Variational Nonsmooth Analysis
Journal: Nonlinear Analysis
Reference: 127 (2015), 157--181.
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Moreau sweeping process with bounded truncated retraction
Author(s):Thibault
Related research area(s): Differential Inclusions, Variational Nonsmooth Analysis
Journal: Journal of Convex Analysis
Download: article
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New metric properties for prox-regular sets
Author(s):Adly, Nacry, Thibault
Related research area(s): Variational Nonsmooth Analysis
Journal: Mathematical Programming
Reference: 189 (2021), 7--36.
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Nonconvex sweeping process and prox-regularity in Hilbert space
Related research area(s): Differential Inclusions, Variational Nonsmooth Analysis
Journal: Journal of Nonlinear and Convex Analysis
Reference: 6 (2005), 359--374.
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On characterizations of submanifolds via smoothness of the distance function in Hilbert spaces
Related research area(s): Differential geometry , Variational Nonsmooth Analysis
Journal: Journal of Optimization Theory and Applications
Reference: 182 (2019), 189--210.
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On generalized differentials and subdifferentials of Lipschitz vector-valued functions
Author(s):Thibault
Related research area(s): Variational Nonsmooth Analysis
Journal: Nonlinear Analysis
Reference: 6 (1982), 1037--1053.
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On proto-differntaibility and strict proto-differentiability of multifunctions of feasible points in perturbed optimization problems
Related research area(s): Variational Nonsmooth Analysis
Journal: Numerical Functional Analysis and Optimization
Reference: 16 (1995), 1293--1307.
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On smoothness of solutions to projected differential equations
Author(s):Salas, Thibault, Vilches
Related research area(s): Differential Inclusions, Variational Nonsmooth Analysis
Journal: Discrete and continuous dynamical systems- Series A
Reference: 39 (2019), 2255--2283.
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On subdifferentials of optimal value functions
Author(s):Thibault
Related research area(s): Optimization, Variational Nonsmooth Analysis
Journal: SIAM Journal on Control and Optimization
Reference: 29 (1991), 1019--1036.
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On the discretization of truncated integro-differential sweeping process and optimal control
Author(s):Bouach, Haddad, Thibault
Related research area(s): Differential Inclusions, Optimal Control , Variational Nonsmooth Analysis
Journal: Journal of Optimization Theory and Applications
Reference: 193 (2022), 785--830.
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On various notions of regularity of sets in nonsmooth analysis
Related research area(s): Variational Nonsmooth Analysis
Journal: Nonlinear Analysis
Reference: 48 (2002), 223--246.
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Partial extensions of Attouch's theorem with applications to proto-derivatives of subgradient mappings
Author(s):Levy, Poliquin, Thibault
Related research area(s): Set-Valued Analysis, Variational Nonsmooth Analysis
Journal: Transactions of American Mathematical Society
Reference: 347 (1995), 1269--1294.
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Perturbed sweeping process with a subsmooth set depending on the state
Author(s):Haddad, Noel, Thibault
Related research area(s): Differential Inclusions, Variational Nonsmooth Analysis
Journal: Linear and Nonlinear Analysis
Reference: 2 (2016), 155--174.
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Preservation of uniform prox-regularity and application to constrained optimization
Author(s):Adly, Nacry, Thibault
Related research area(s): Optimization, Variational Nonsmooth Analysis
Journal: SIAM Journal on Optimization
Reference: 26 (2016), 448--473.
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Primal-lower-nice property of value functions in optimization and control problems
Related research area(s): Optimization, Variational Nonsmooth Analysis
Journal: Set-Valued and Variational Analysis
Reference: 18 (2010), 569--600.
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Problèmes de Bolza dans un espace de Banach séparable
Author(s):Thibault
Related research area(s): Variational Nonsmooth Analysis
Journal: Comptes Rendus de l'Académie des Sciences de Paris
Reference: 282 (1976), 1303--1306.
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Prox-regular functions in Hilbert space
Related research area(s): Variational Nonsmooth Analysis
Journal: Journal of Mathematical Analysis and Applications
Reference: 303 (2005), 1--14.
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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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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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Prox-regularity approach to generalized equations and image projection
Author(s):Adly, Nacry, Thibault
Related research area(s): Set-Valued Analysis, Variational Nonsmooth Analysis
Journal: ESAIM Control Optim. Calc. Var.
Reference: 24 (2018), 677--708.
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Prox-regularity of functions and sets in Banach spaces
Related research area(s): Variational Nonsmooth Analysis
Journal: Set-Valued Analysis
Reference: 12 (2004), 25--47.
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Proximal and Fréchet normal formulae for some small normal cones
Related research area(s): Variational Nonsmooth Analysis
Journal: Nonlinear Analysis
Reference: 19 (1992), 599--612.
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Qualification conditions for calculus rules of coderivatives of multivalued mappings
Related research area(s): Set-Valued Analysis, Variational Nonsmooth Analysis
Journal: Journal of Mathematical Analysis and Applications
Reference: 218 (1998), 66--81.
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Quantitative characterizations of nonconvex bodies with smooth boundaries in Hilbert spaces va the metric projection
Related research area(s): Variational Nonsmooth Analysis
Journal: Journal of Mathematical Analysis and Applications
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Quasi-interiorly e-tangent cones to multifunctions
Author(s):El Abdouni, Thibault
Related research area(s): Set-Valued Analysis, Variational Nonsmooth Analysis
Journal: Numerical Functional Analysis and Optimization
Reference: 10 (1989), 619--641.
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Quelques propriétés des sous-différentiels de fonctions réelles localement lipschitziennes définies sur un espace de Banach séparable
Author(s):Thibault
Related research area(s): Variational Nonsmooth Analysis
Journal: Comptes Rendus de l'Académie des Sciences de Paris
Reference: 282 (1976), 507--510.
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Reduction of state dependent sweeping process to unsconstrained differential inclusion
Author(s):Haddad, Kecis, Thibault
Related research area(s): Differential Inclusions, Set-Valued Analysis, Variational Nonsmooth Analysis
Journal: Journal of Global Optimization
Reference: 62 (2015), 167--182.
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Regularization of dynamical systems associated with prox-regular moving sets
Related research area(s): Differential Inclusions, Set-Valued Analysis, Variational Nonsmooth Analysis
Journal: Journal of Nonlinear and Convex Analysis
Reference: 15 (2014), 647--663.
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Scalarization of tangential regularity of set-valued mappings
Author(s):Thibault
Related research area(s): Set-Valued Analysis, Variational Nonsmooth Analysis
Journal: Set-Valued Analysis
Reference: 7 (1999), 33--53.
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Smoothness of the metric projection onto nonconvex bodies in Hilbert spaces
Author(s):Correa, Salas, Thibault
Related research area(s): Variational Nonsmooth Analysis
Journal: Journal of Mathematical Analysis and Applications
Reference: 457 (2018), 1307--1332.
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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 characterization of s-lower regular functions
Related research area(s): Variational Nonsmooth Analysis
Journal: Applicable Analysis
Reference: 94 (2015), 85--98.
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Subdifferential determination of essentially directionally smooth functions in Banach space
Related research area(s): Functional analysis, Variational Nonsmooth Analysis
Journal: SIAM Journal on Optimization
Reference: 20 (2010), 2300--2326.
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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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Subdifferential regularity of directionally Lipschitzian functions
Related research area(s): Variational Nonsmooth Analysis
Journal: Canadian Mathematical Bulletin
Reference: 43 (2000), 25--36.
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Subdifferential representation formula annd subdifferential criteria for the behavior of nonsmooth functions
Author(s):Correa, Gajardo, Thibault
Related research area(s): Variational Nonsmooth Analysis
Journal: Nonlinear Analysis
Reference: 65 (2006), 864--891.
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Subdifferentials of compactly Lipschitzian vector-valued functions
Author(s):Thibault
Related research area(s): Variational Nonsmooth Analysis
Journal: Annali di Matematica Pura ed Applicata
Reference: 125 (1980), 157--192.
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Subdifferentials of nonconvex vector-valued functions
Author(s):Thibault
Related research area(s): Variational Nonsmooth Analysis
Journal: Journal of Mathematical Analysis and Applications
Reference: 86 (1982), 319--344.
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Sublevel representation of epi-Lipschitz sets and other properties
Related research area(s): Optimization, Set-Valued Analysis, Variational Nonsmooth Analysis
Journal: Mathematical Programming
Reference: 168 (2018), 555--569.
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Subsmooth sets: Functional characterizations and related topics
Author(s):Aussel, Daniilidis, Thibault
Related research area(s): Variational Nonsmooth Analysis
Journal: Transactions of American Mathematical Society
Reference: 357 (2005), 1275--1301.
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Sweeping process with regular and nonregular sets
Author(s):Thibault
Related research area(s): Differential Inclusions, Variational Nonsmooth Analysis
Journal: Journal of Differential Equations
Reference: 54 (2003), 1251--1269.
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Tangent cones and quasi-interiorly tangent cones to multifunctions
Author(s):Thibault
Related research area(s): Variational Nonsmooth Analysis
Journal: Transactions of American Mathematical Society
Reference: 277 (1983), 601--621.
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The approximate subdifferential of composite functions
Related research area(s): Set-Valued Analysis, Variational Nonsmooth Analysis
Journal: Bulletin of Australian Mathematical Society
Reference: 47 (1993), 443--455.
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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.
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The use of metric graphical regularity in approximate subdifferential calculus rules in finite dimensions
Related research area(s): Variational Nonsmooth Analysis
Journal: Optimization
Reference: 21 (1990), 509--519.
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Uniformly prox-regularity of functions and epigraphs in Hilbert spaces
Related research area(s): Variational Nonsmooth Analysis
Journal: Nonlinear Analysis
Reference: 60 (2005), 187--207.
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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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Various Lipschitz-like properties for functions and sets II: subdifferential and normal characterizations
Author(s):Correa, Gajardo, Thibault
Related research area(s): Set-Valued Analysis, Variational Nonsmooth Analysis
Journal: Journal of Convex Analysis
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Verifiable conditions for openness and regularity of multivalued mappings in Banch spaces
Related research area(s): Set-Valued Analysis, Variational Nonsmooth Analysis
Journal: Transactions of American Mathematical Society
Reference: 347 (1995), 1255--1268.
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Well-posedness and subdifferentials of optimal value and infimal convolution
Related research area(s): Optimization, Variational Nonsmooth Analysis
Journal: Set-Valued and Variational Analysis
Reference: 27 (2019), 841--861.