Thibault, Lionel

Related book(s)

• Prox-Regular Sets and Applications

  Authors: Colombo, Thibault

  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.

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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.

  More details

  cover

Related talk(s)

• Lipschitz perturbation of BV-sweeping process

  Authors: Thibault

  Talk presented in ''Journees annuelles: Mathematiques de l'Optimisation et Applications, Paris june 2013"

  Download the presentation

Related article(s)

• 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.

• A note on Fréchet and approximate subdifferentials of composite functions

  Author(s):Jourani, Thibault

  Related research area(s): Variational Nonsmooth Analysis

  Journal: Bulletin of Australian Mathematical Society

  Reference: 49 (1994), 111--115.

• A note on subdifferentials of convex composite functionals

  Author(s):Laghdir, Thibault

  Related research area(s): Modern Convex Analysis

  Journal: Archiv der Mathematik

  Reference: 67 (1996), 239--252.

• 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.

• 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.

• Approximate and metric regularity in mathematical programming in Banach space

  Author(s):Jourani, Thibault

  Related research area(s): Optimization, Variational Nonsmooth Analysis

  Journal: Mathematics of Operations research

  Reference: 18 (1993), 390--401.

• Approximate subdifferential and metric regularity: the finite-dimensional case

  Author(s):Jourani, Thibault

  Journal: Mathematical Programming

  Reference: 47 (1990), 203--218.

• b-Subgradients of the optimal value function in nonlinear programming

  Author(s):Jofré, Thibault

  Related research area(s): Optimization

• Bolza type problems in discrete time

  Author(s):Sahraoui, Thibault

  Related research area(s): Optimal Control

  Journal: Taiwanese Journal of Mathematics

  Reference: 12 (2008), 1385--1400.

• BV prox-regular sweeping process with bounded truncation

  Author(s):Nacry, Thibault

  Related research area(s): Differential Inclusions, Variational Nonsmooth Analysis

  Journal: Optimization

  Reference: 69 (2020), 1391--1437.

• BV solutions of nonconvex sweeping process differential inclusion with perturbation

  Author(s):Edmond, Thibault

  Related research area(s): Differential Inclusions

  Journal: Journal of Differential Equations

  Reference: 226 (2006), 135--179.

• 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.

• Chain rules for coderivatives of multivalued mappings in Banach spaces

  Author(s):Jourani, Thibault

  Related research area(s): Set-Valued Analysis, Variational Nonsmooth Analysis

  Journal: Proceedings of American Mathematical Society

  Reference: 126 (1998), 1479--1485.

• 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.

• 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.

• Coderivative of multivalued mappings, locally compact cones and metric regularity

  Author(s):Jourani, Thibault

  Related research area(s): Variational Nonsmooth Analysis

  Journal: Nonlinear Analysis

  Reference: 35 (1999), 925--945.

• 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.

• Continuity of measurable convex and biconvex operators

  Author(s):Thibault

  Related research area(s): Modern Convex Analysis

• 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.

• 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.

• D-representation of subdifferentials of directionally Lipschitz functions

  Author(s):Jofré, Thibault

  Related research area(s): Modern Convex Analysis, Variational Nonsmooth Analysis

  Journal: Proceedings of American Mathematical Society

  Reference: 110 (1990), 117--123.

• 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.

• Directional derivatives and almost everywhere differentiability of biconvex and concave-convex operators

  Author(s):Jouak, Thibault

  Related research area(s): Modern Convex Analysis

  Journal: Mathematica Scandinavica

  Reference: 57 (1985), 215--224.

• Directionally pseudo-Lipschitz set-valued mappings

  Author(s):Bounkhel, Thibault

  Related research area(s): Variational Nonsmooth Analysis

  Journal: Journal of Mathematical Analysis and Applications

  Reference: 266 (2002), 269--287.

• 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.

• Distance function associated to a prox-regular set

  Author(s):Nacry, Thibault

  Related research area(s): Variational Nonsmooth Analysis

  Journal: Set-Valued and Variational Analysis

  Reference: 30 (2022), 731--750.

• Enlarged inclusions of subdifferentials

  Author(s):Thibault, Zagrodny

  Related research area(s): Set-Valued Analysis, Variational Nonsmooth Analysis

  Journal: Canadian Mathematical Bulletin

  Reference: 48 (2005), 283--301.

• 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.

• 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.

• 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.

• Epiconvergence of convexly composite functions in Banach spaces

  Author(s):Combari, Thibault

  Related research area(s): Modern Convex Analysis, Variational Nonsmooth Analysis

  Journal: SIAM Journal on Optimization

  Reference: 13 (2003), 986--1003.

• Equicontinuity of families of convex and concave-convex operators

  Author(s):Jouak, Thibault

  Related research area(s): Modern Convex Analysis

  Journal: Canadian Journal of Mathematics

  Reference: 36 (1984), 883--898.

• 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.

• Espérances conditionnelles d'intégrandes semi-continus

  Author(s):Thibault

  Related research area(s): Set-Valued Analysis

  Journal: Annales Institut Henri Poincaré

  Reference: 17 (1981), 337--350.

  Excitavit hic ardor milites per municipia plurima, quae isdem conterminant, dispositos et castella, sed quisque serpentes latius pro viribus repellere moliens, nunc globis confertos, aliquotiens et dispersos multitudine superabatur ingenti, quae nata et educata inter editos recurvosque ambitus montium eos ut loca plana persultat et mollia, missilibus obvios eminus lacessens et ululatu truci perterrens.

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• Evolution differential inclusions associated to primla lower regular functions

  Author(s):Kecis, Thibault

  Related research area(s): Differential Inclusions, Set-Valued Analysis, Variational Nonsmooth Analysis

  Journal: Journal of Nonlinear and Convex Analysis

  Reference: 20 (2019), 1949--1979.

• Evolution problems associated with primal lower nice functions

  Author(s):Marcellin, Thibault

  Related research area(s): Set-Valued Analysis, Variational Nonsmooth Analysis

  Journal: Journal of Convex Analysis

  Reference: 13 (2006), 385--421.

• Existence and relaxation theorem for a second order differential inclusion

  Author(s):Azzam-Laouir, Makhlouf, Thibault

  Related research area(s): Differential Inclusions

  Journal: Numerical Functional Analysis and Optimization

  Reference: 31 (2010), 1103--1119.

• Existence and uniqueness of solutions for non-autonomous complementarity dynamical systems

  Author(s):Brogliato, Thibault

  Related research area(s): Differential Inclusions

  Journal: Journal of Convex Analysis

  Reference: 17 (2010), 961--990.

• 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.

• Existence of solutions for second-order differential inclusion with nonconvex perturbations

  Author(s):Azzam-Laouir, Lounis, Thibault

  Related research area(s): Differential Inclusions

  Journal: Applicable Analysis

  Reference: 86 (2007), 1199--1210.

• Extensions of subdifferential calculus rules in Banach spaces

  Author(s):Jourani, Thibault

  Related research area(s): Variational Nonsmooth Analysis

  Journal: Canadian Journal of Mathematics

  Reference: 48 (1996), 183--201.

• Familles équilipschitziennes d'applications convexes ou biconvexes vectorielles

  Author(s):Jouak, Thibault

  Related research area(s): Modern Convex Analysis

  Journal: Comptes Rendus de l'Académie des Sciences de Paris

  Reference: 298 (1984), 83--85.

• 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.

• Functional evolution equations governed by nonconvex sweeping process

  Author(s):Castaing , Salvadori, Thibault

  Related research area(s): Differential Inclusions, Optimal Control

  Journal: Journal of Nonlinear and Convex Analysis

  Reference: 2 (2001), 217--241.

• Inclusion and integration of subdifferentials

  Author(s):Edmond, Thibault

  Related research area(s): Variational Nonsmooth Analysis

  Journal: Journal of Nonlinear and Convex Analysis

  Reference: 3 (2002), 411--434.

• Inclusion of Subdifferentials, Linear Well-Conditioning, and Steepest Descent Equation

  Author(s):Cabot, Thibault

  Related research area(s): Differential Inclusions

  Journal: SIAM Journal on Optimization

  Reference: 23 (2013), 552--575.

  Excitavit hic ardor milites per municipia plurima, quae isdem conterminant, dispositos et castella, sed quisque serpentes latius pro viribus repellere moliens, nunc globis confertos, aliquotiens et dispersos multitudine superabatur ingenti, quae nata et educata inter editos recurvosque ambitus montium eos ut loca plana persultat et mollia, missilibus obvios eminus lacessens et ululatu truci perterrens.

• Infimal convolution and optimal time control problem I: Frechet and proximal subdifferential

  Author(s):Ivanov, Thibault

  Related research area(s): Optimization, Variational Nonsmooth Analysis

  Journal: Set-Valued and Variational Analysis

  Reference: 26 (2018), 581--606.

• Infimal convolution and optimal time control problem II: limiting subdifferential

  Author(s):Ivanov, Thibault

  Related research area(s): Optimization, Variational Nonsmooth Analysis

  Journal: Set-Valued and Variational Analysis

  Reference: 25 (2017), 517--542.

• Infimal convolution and optimal time control problem III: minimal time projection set

  Author(s):Ivanov, Thibault

  Related research area(s): Optimization, Variational Nonsmooth Analysis

  Journal: SIAM Journal on Optimization

  Reference: 28 (2018), 30--44.

• Integrability of subdifferentials of certain bivariate functions

  Author(s):Thibault, Zlateva

  Related research area(s): Modern Convex Analysis, Variational Nonsmooth Analysis

  Journal: Nonlinear Analysis

  Reference: 54 (2003), 1251--1269.

• Integrability of subdifferentials of directionally Lipschitz functions

  Author(s):Thibault, Zlateva

  Related research area(s): Variational Nonsmooth Analysis

  Journal: Proceedings of American Mathematical Society

  Reference: 133 (2005), 2939--2948.

• Integration of epsilon-Fenchel subdifferentials and maximal cyclic monotonicity

  Author(s):Marcellin, Thibault

  Related research area(s): Modern Convex Analysis

  Journal: Journal of Global Optimization

  Reference: 32 (2005), 83--91.

• 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.

• Integration of subdifferentials oof lower semicontinuous functions on Banach spaces

  Author(s):Thibault, Zagrodny

  Related research area(s): Variational Nonsmooth Analysis

  Journal: Journal of Mathematical Analysis and Applications

  Reference: 189 (1995), 33--58.

• Lagrange multipliers for Pareto nonsmooth programming problems in Banach spaces

  Author(s):El Abdouni, Thibault

  Related research area(s): Optimization

  Journal: Optimization

  Reference: 26 (1992), 277--285.

• 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.

• 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.

• Metric projection and compatibly parameterized families of prox-regular sets in Hilbert space

  Author(s):Sebbah, Thibault

  Related research area(s): Variational Nonsmooth Analysis

  Journal: Nonlinear Analysis

  Reference: 75 (2012), 1547--1562.

• Metric regularity and subdifferential calculus in Banach space

  Author(s):Jourani, Thibault

  Related research area(s): Variational Nonsmooth Analysis

  Journal: Set-Valued Analysis

  Reference: 3 (1995), 87--100.

• Metric regularity for strongly compactly Lipschitzian mappings

  Author(s):Jourani, Thibault

  Related research area(s): Optimization, Variational Nonsmooth Analysis

  Journal: Nonlinear Analysis

  Reference: 24 (1995), 229--240.

• Moreau envelopes of s-lower regular functions

  Author(s):Kecis, Thibault

  Related research area(s): Variational Nonsmooth Analysis

  Journal: Nonlinear Analysis

  Reference: 127 (2015), 157--181.

• Moreau sweeping process with bounded truncated retraction

  Author(s):Thibault

  Related research area(s): Differential Inclusions, Variational Nonsmooth Analysis

  Journal: Journal of Convex Analysis

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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.

• Non coincidence of approximate and limiting subdifferentials of integral functionals

  Author(s):Jourani, Thibault

  Related research area(s): Optimal Control

  Journal: SIAM Journal on Control and Optimization

  Reference: 49 (2011), 1435--1453.

  For a locally Lipschitz integral functional defines on the space of integrable functions, the limiting subdifferential and the approximate subdifferential never coincide at a point where the integrand is not subdifferentially regular almost everywhere. The coincidence of both subdifferentials occurs on a dense set of the space of integrable functions if and only if the integrand is a convex integrand. Our results allow us to obtain Aubin's Lipschitz-like property as well as the convexity of multivalued mappings between the spaces of integrable functions. New necessary optimality conditions for some Bolza problems are also obtained.

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• Nonconvex sweeping process and prox-regularity in Hilbert space

  Author(s):Bounkhel, Thibault

  Related research area(s): Differential Inclusions, Variational Nonsmooth Analysis

  Journal: Journal of Nonlinear and Convex Analysis

  Reference: 6 (2005), 359--374.

• On characterizations of submanifolds via smoothness of the distance function in Hilbert spaces

  Author(s):Salas, Thibault

  Related research area(s): Differential geometry , Variational Nonsmooth Analysis

  Journal: Journal of Optimization Theory and Applications

  Reference: 182 (2019), 189--210.

• 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.

• On proto-differntaibility and strict proto-differentiability of multifunctions of feasible points in perturbed optimization problems

  Author(s):Amahroq, Thibault

  Related research area(s): Variational Nonsmooth Analysis

  Journal: Numerical Functional Analysis and Optimization

  Reference: 16 (1995), 1293--1307.

• 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.

• 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.

• 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.

• 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.

• 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.

• On the graph convergence of subdifferentials of convex functions

  Author(s):Combari, Thibault

  Related research area(s): Modern Convex Analysis

  Journal: Proceedings of American Mathematical Society

  Reference: 126 (1998), 2231--2240.

• On various notions of regularity of sets in nonsmooth analysis

  Author(s):Bounkhel, Thibault

  Related research area(s): Variational Nonsmooth Analysis

  Journal: Nonlinear Analysis

  Reference: 48 (2002), 223--246.

• Optimality conditions for problems with set-valued objectives

  Author(s):El Abdouni, Thibault

  Related research area(s): Optimization, Set-Valued Analysis

  Journal: Journal of Applied Analysis

  Reference: 2 (1996), 183--201.

• 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.

• Partially ball weakly inf-compact saddle functions

  Author(s):Thibault, Zagrodny

  Related research area(s): Modern Convex Analysis

  Journal: Mathematics of Operations research

  Reference: 30 (2005), 404--419.

• 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

  Author(s):Serea, Thibault

  Related research area(s): Optimization, Variational Nonsmooth Analysis

  Journal: Set-Valued and Variational Analysis

  Reference: 18 (2010), 569--600.

• 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.

• Prox-regular functions in Hilbert space

  Author(s):Bernard, Thibault

  Related research area(s): Variational Nonsmooth Analysis

  Journal: Journal of Mathematical Analysis and Applications

  Reference: 303 (2005), 1--14.

• 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.

• 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.

• 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.

• Prox-regularity of functions and sets in Banach spaces

  Author(s):Bernard, Thibault

  Related research area(s): Variational Nonsmooth Analysis

  Journal: Set-Valued Analysis

  Reference: 12 (2004), 25--47.

• Proximal and Fréchet normal formulae for some small normal cones

  Author(s):Jofré, Thibault

  Related research area(s): Variational Nonsmooth Analysis

  Journal: Nonlinear Analysis

  Reference: 19 (1992), 599--612.

• Qualification conditions for calculus rules of coderivatives of multivalued mappings

  Author(s):Jourani, Thibault

  Related research area(s): Set-Valued Analysis, Variational Nonsmooth Analysis

  Journal: Journal of Mathematical Analysis and Applications

  Reference: 218 (1998), 66--81.

• Quantitative characterizations of nonconvex bodies with smooth boundaries in Hilbert spaces va the metric projection

  Author(s):Salas, Thibault

  Related research area(s): Variational Nonsmooth Analysis

  Journal: Journal of Mathematical Analysis and Applications

• 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.

• 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.

• 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.

• Reduction of sweeping process to unconstrained differential inclusion

  Author(s):Haddad, Jourani, Thibault

  Related research area(s): Differential Inclusions

  Journal: Pacific Journal of Optimization

  Reference: 4 (2008), 493--512.

• Regularization of dynamical systems associated with prox-regular moving sets

  Author(s):Sene, Thibault

  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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• Regularization of nonconvex sweeping process in Hilbert space

  Author(s):Thibault

  Related research area(s): Differential Inclusions

  Journal: Set-Valued Analysis

  Reference: 16 (2008), 319--333.

• Relaxation of an optimal control problem involving a perturbed sweeping process

  Author(s):Edmond, Thibault

  Related research area(s): Differential Inclusions, Optimal Control

  Journal: Mathematical Programming

  Reference: 104 (2005), 347--373.

• 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.

• 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.

• Sequential formulae for the normal cone to sublevel sets

  Author(s):Cabot, Thibault

  Related research area(s): Modern Convex Analysis

  Journal: Transactions of American Mathematical Society

  Reference: 366 (2014), 6591--6628.

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• Sequential of integral sum of convex functions

  Author(s):Lopez, Thibault

  Related research area(s): Modern Convex Analysis

  Journal: Journal of Nonlinear and Convex Analysis

  Reference: 9 (2008), 295--308.

• 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.

• 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.

• Strict approximate solutions in set-valued optimization with applications to the approximate Ekeland variational principle

  Author(s):Gutiérrez, Jiménez, Novo, Thibault

  Related research area(s): Optimization, Set-Valued Analysis

  Journal: Nonlinear Analysis

  Reference: 73 (2010), 3842--3855.

• Subdifferential analysis of bivariate separately regular functions

  Author(s):Correa, Thibault

  Related research area(s): Modern Convex Analysis, Variational Nonsmooth Analysis

  Journal: Journal of Mathematical Analysis and Applications

  Reference: 148 (1990), 157--174.

• Subdifferential characterization of s-lower regular functions

  Author(s):Kecis, Thibault

  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

  Author(s):Thibault, Zagrodny

  Related research area(s): Functional analysis, Variational Nonsmooth Analysis

  Journal: SIAM Journal on Optimization

  Reference: 20 (2010), 2300--2326.

• 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.

• Subdifferential regularity of directionally Lipschitzian functions

  Author(s):Bounkhel, Thibault

  Related research area(s): Variational Nonsmooth Analysis

  Journal: Canadian Mathematical Bulletin

  Reference: 43 (2000), 25--36.

• 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.

• 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.

• 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.

• Sublevel representation of epi-Lipschitz sets and other properties

  Author(s):Czarnecki, Thibault

  Related research area(s): Optimization, Set-Valued Analysis, Variational Nonsmooth Analysis

  Journal: Mathematical Programming

  Reference: 168 (2018), 555--569.

• 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.

• 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.

• 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.

• The approximate subdifferential of composite functions

  Author(s):Jourani, Thibault

  Related research area(s): Set-Valued Analysis, Variational Nonsmooth Analysis

  Journal: Bulletin of Australian Mathematical Society

  Reference: 47 (1993), 443--455.

• 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.

• 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.

• The use of metric graphical regularity in approximate subdifferential calculus rules in finite dimensions

  Author(s):Jourani, Thibault

  Related research area(s): Variational Nonsmooth Analysis

  Journal: Optimization

  Reference: 21 (1990), 509--519.

• Three boundary value problems fo second order differential inclusions

  Author(s):Azzam-Laouir, Castaing , Thibault

  Related research area(s): Differential Inclusions

  Journal: Control and Cybernetics

  Reference: 31 (2002), 659--693.

• Uniformly prox-regularity of functions and epigraphs in Hilbert spaces

  Author(s):Bernard, Thibault

  Related research area(s): Variational Nonsmooth Analysis

  Journal: Nonlinear Analysis

  Reference: 60 (2005), 187--207.

• 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.

• Variational convergence of composed convex functions

  Author(s):Laghdir, Thibault

  Related research area(s): Modern Convex Analysis, Optimization

  Journal: Journal of Positivity

  Reference: 9 (2005), 115--147.

• 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.

• 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

• Verifiable conditions for openness and regularity of multivalued mappings in Banch spaces

  Author(s):Jourani, Thibault

  Related research area(s): Set-Valued Analysis, Variational Nonsmooth Analysis

  Journal: Transactions of American Mathematical Society

  Reference: 347 (1995), 1255--1268.

• Viability for constrained stochastic differential equations

  Author(s):Gautier, Thibault

  Related research area(s): Differential Inclusions, Set-Valued Analysis

  Journal: Differential Integral Equations

  Reference: 6 (1993), 1395--1414.

• 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.

• Well-posedness and subdifferentials of optimal value and infimal convolution

  Author(s):Ivanov, Thibault

  Related research area(s): Optimization, Variational Nonsmooth Analysis

  Journal: Set-Valued and Variational Analysis

  Reference: 27 (2019), 841--861.