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Differential Inclusions
I am mainly interested in differential inclusions associated with ''sweeping processes''. Such differential inclusions involve the normal cone of a closed moving set depending on the time.
Related article(s)
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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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BV solutions of nonconvex sweeping process differential inclusion with perturbation
Related research area(s): Differential Inclusions
Journal: Journal of Differential Equations
Reference: 226 (2006), 135--179.
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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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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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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.
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Existence and uniqueness of solutions for non-autonomous complementarity dynamical systems
Related research area(s): Differential Inclusions
Journal: Journal of Convex Analysis
Reference: 17 (2010), 961--990.
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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.
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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.
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Inclusion of Subdifferentials, Linear Well-Conditioning, and Steepest Descent Equation
Related research area(s): Differential Inclusions
Journal: SIAM Journal on Optimization
Reference: 23 (2013), 552--575.
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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
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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 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 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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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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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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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.
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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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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.
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Relaxation of an optimal control problem involving a perturbed sweeping process
Related research area(s): Differential Inclusions, Optimal Control
Journal: Mathematical Programming
Reference: 104 (2005), 347--373.
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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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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.
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Viability for constrained stochastic differential equations
Related research area(s): Differential Inclusions, Set-Valued Analysis
Journal: Differential Integral Equations
Reference: 6 (1993), 1395--1414.