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Pontryagin maximum principle for general Caputo fractional optimal control problems with Bolza cost and terminal constraints

 Maïtine Bergounioux , Loïc Bourdin
ESAIM: Control, Optimisation and Calculus of Variations, In press
Article dans une revue hal-01796387v2
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Optimal sampled-data controls with running inequality state constraints: Pontryagin maximum principle and bouncing trajectory phenomenon

 Loïc Bourdin , Gaurav Dhar
Mathematical Programming, Series A, 2020
Article dans une revue hal-02160231v2
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Linear-quadratic optimal sampled-data control problems: convergence result and Riccati theory

 Loïc Bourdin , Emmanuel Trélat
Automatica, 2017, 79, pp.273--281
Article dans une revue hal-01304197v1
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Shape optimization for variational inequalities: the scalar Tresca friction problem

 Samir Adly , Loïc Bourdin , Fabien Caubet , Aymeric Jacob de Cordemoy
SIAM Journal on Optimization, 2023, 33 (4), pp.2512-2541
Article dans une revue hal-03848645v4
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On the reduction of a spatially hybrid optimal control problem into a temporally hybrid optimal control problem

 Térence Bayen , Anas Bouali , Loïc Bourdin , Olivier Cots
2023
Pré-publication, Document de travail hal-04319045v1
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Legendre's necessary condition for fractional Bolza functionals with mixed initial/final constraints

 Loïc Bourdin , Rui A. C. Ferreira
Journal of Optimization Theory and Applications, In press
Article dans une revue hal-02568662v4
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Pontryagin-Type Conditions for Optimal Muscular Force Response to Functional Electric Stimulations

 Toufik Bakir , Bernard Bonnard , Loïc Bourdin , Jérémy Rouot
Journal of Optimization Theory and Applications, 2020, 184 (2), pp.581-602. ⟨10.1007/s10957-019-01599-4⟩
Article dans une revue hal-01854551v3
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Existence of Minimizers for Fractional Variational Problems Containing Caputo Derivatives

 Loïc Bourdin , Tatiana Odzijewicz , Delfim F. M. Torres
Advances in Dynamical Systems and Applications, 2013, 8 (1), pp.3-12
Article dans une revue hal-01253289v1
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Flip procedure in geometric approximation of multiple-component shapes – Application to multiple-inclusion detection

 Pierre Bonnelie , Loïc Bourdin , Fabien Caubet , Olivier Ruatta
SMAI Journal of Computational Mathematics, 2016, 2, pp.255-276
Article dans une revue hal-01710845v1
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Direct and Indirect Methods to Optimize the Muscular Force Response to a Pulse Train of Electrical Stimulation

 Toufik Bakir , Bernard Bonnard , Loïc Bourdin , Jérémy Rouot
ESAIM: Proceedings and Surveys, 2021, 71, pp.1-10. ⟨10.1051/proc/202171101⟩
Article dans une revue hal-02053566v2
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Sensitivity Analysis of a Scalar Mechanical Contact Problem with Perturbation of the Tresca's Friction Law

 Loïc Bourdin , Fabien Caubet , Aymeric Jacob de Cordemoy
Journal of Optimization Theory and Applications, 2022, 192, pp.856-890
Article dans une revue hal-03561843v2
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Helmholtz's inverse problem of the discrete calculus of variations

 Loïc Bourdin , Jacky Cresson
Journal of Difference Equations and Applications, 2013, 19 (9), pp.1417-1436. ⟨10.1080/10236198.2012.754435⟩
Article dans une revue hal-00866945v1
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On a decomposition formula for the proximal operator of the sum of two convex functions

 Samir Adly , Loïc Bourdin , Fabien Caubet
Journal of Convex Analysis, 2019, 26 (2), pp.699-718
Article dans une revue hal-01558522v2

Existence of minimizers for generalized Lagrangian functionals and a necessary optimality condition - Application to fractional variational problems

 Loïc Bourdin , Tatiana Odzijewicz , Delfim Torres
Differential and integral equations, 2014, 27 (7-8), pp.743-766. ⟨10.1155/2012/871912]⟩
Article dans une revue hal-01253284v2
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Optimal sampled-data control, and generalizations on time scales

 Loïc Bourdin , Emmanuel Trélat
Mathematical Control and Related Fields, 2016, 6 (1), pp.53--94
Article dans une revue hal-01110750v2
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Hybrid maximum principle with regionally switching parameter

 Térence Bayen , Anas Bouali , Loïc Bourdin
2022
Pré-publication, Document de travail hal-03638701v1

A fractional fundamental lemma and a fractional integration by parts formula – Applications to critical points of Bolza functionals and to linear boundary value problems

 Loïc Bourdin , Dariusz Idczak
Advances in Differential Equations, 2015, 20 (3-4), pp.213-232
Article dans une revue hal-01253280v3

Integrative river science and rehabilitation : European experiences

 Hervé Piégay , L. A. Naylor , G. Haidvogl , J. Kail , L. Schmitt , et al.
Brierley, Gary J.;Fryirs, Kirstie A.;. River futures : an integrative scientific approach to river repair, Society for Ecological Restoration International, pp.201 -219, 2008
Chapitre d'ouvrage halshs-00435355v1

On a Decomposition Formula for the Resolvent Operator of the Sum of Two Set-Valued Maps with Monotonicity Assumptions

 Samir Adly , Loïc Bourdin
Applied Mathematics and Optimization, 2019, 80 (3), pp.715--732. ⟨10.1007/s00245-019-09599-6⟩
Article dans une revue hal-02386009v1
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Unified Riccati theory for optimal permanent and sampled-data control problems in finite and infinite time horizons

 Loïc Bourdin , Emmanuel Trélat
SIAM Journal on Control and Optimization, 2021, 59 (2), pp.489--508. ⟨10.1137/20M1318535⟩
Article dans une revue hal-02473706v1
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Existence of a weak solution for fractional Euler–Lagrange equations

 Loïc Bourdin
Journal of Mathematical Analysis and Applications, 2013, 399 (1), pp.239-251. ⟨10.1016/j.jmaa.2012.10.008⟩
Article dans une revue hal-01253291v1
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Addendum to Pontryagin's maximum principle for dynamic systems on time scales

 Loïc Bourdin , Oleksandr Stanzhytskyi , Emmanuel Trélat
Journal of Difference Equations and Applications, 2017, 23 (10), pp.1760-1763. ⟨10.1080/10236198.2017.1363194⟩
Article dans une revue hal-01674566v1

Cauchy-Lipschitz theory for fractional multi-order dynamics -- State-transition matrices, Duhamel formulas and duality theorems

 Loïc Bourdin
Differential and integral equations, 2018, 31 (7-8)
Article dans une revue hal-01558524v2
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Pontryagin maximum principle for optimal sampled-data control problems

 Loïc Bourdin , Emmanuel Trélat
The 16th IFAC Workshop on Control Applications of Optimization (CAO'2015), Oct 2015, Garmisch-Partenkirchen, Germany. ⟨10.1016/j.ifacol.2015.11.063⟩
Communication dans un congrès hal-01238220v1
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Note on Pontryagin maximum principle with running state constraints and smooth dynamics - Proof based on the Ekeland variational principle

 Loïc Bourdin
[0] University of Limoges, France. 2016
Rapport hal-01302222v1
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General Cauchy-Lipschitz theory for Δ-Cauchy problems with Carathéodory dynamics on time scales

 Loïc Bourdin , Emmanuel Trélat
Journal of Difference Equations and Applications, 2014, 20 (4), pp.526--547
Article dans une revue hal-00767661v1
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Variational integrators of fractional Lagrangian systems in the framework of discrete embeddings

 Loïc Bourdin , Jacky Cresson , Isabelle Greff , Pierre Inizan
11ème conférence internationale Saragosse-Pau sur les Mathématiques Appliquées, 2010, Jaca, Spain
Communication dans un congrès hal-00868514v1
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Nonshifted calculus of variations on time scales with ∇-differentiable σ

 Loïc Bourdin
Journal of Mathematical Analysis and Applications, 2014, 411 (2), pp.543-554. ⟨10.1016/j.jmaa.2013.10.013⟩
Article dans une revue hal-01253287v1
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Variational integrator for fractional Euler–Lagrange equations

 Loïc Bourdin , Jacky Cresson , Isabelle Greff , Pierre Inizan
Applied Numerical Analysis and Computational Mathematics, 2013, 71, pp.14-23. ⟨10.1016/j.apnum.2013.03.003⟩
Article dans une revue hal-00866948v1
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The derivative of a parameterized mechanical contact problem with a Tresca's friction law involves Signorini unilateral conditions

 Samir Adly , Loïc Bourdin , Fabien Caubet
2019
Pré-publication, Document de travail hal-02368180v1
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