Possible approaches for the dynamic programming method ,
Control Theory from the Geometric Viewpoint. Control theory and optimization, 2004. ,
Introduction to Numerical Continuation Methods Asymptotic expansions for interior penalty solutions of control constrained linear-quadratic problems, Society for Industrial and Applied Mathematics Math. Program, vol.135, pp.1-2473, 2003. ,
Functions of bounded variation and free discontinuity problems. Oxford Mathematical Monographs, 2000. ,
Second order analysis of optimal control problems with singular arcs, 2011. ,
URL : https://hal.archives-ouvertes.fr/tel-00682276
Set-Valued Analysis, Systems & Control. Birkhäuser, 1990. ,
Lectures on Young measure theory and its applications in economics, 1998. ,
Relaxation of Constrained Control Problems, SIAM Journal on Control and Optimization, vol.34, issue.6, pp.2077-2091, 1996. ,
DOI : 10.1137/S036301299427432X
Sensitivity analysis for the outages of nuclear power plants, Energy Systems, vol.97, issue.2, 2012. ,
DOI : 10.1007/s12667-013-0096-y
URL : https://hal.archives-ouvertes.fr/hal-00671186
Survey of Numerical Methods for Trajectory Optimization, Journal of Guidance, Control, and Dynamics, vol.21, issue.2, pp.193-207, 1998. ,
DOI : 10.2514/2.4231
The shooting approach to optimal control problems, Proc. IFAC International Workshop on Adaptation and Learning in Control and Signal Processing ,
DOI : 10.3182/20130703-3-FR-4038.00158
URL : https://hal.archives-ouvertes.fr/hal-00830896
Perturbed Optimization in Banach Spaces I: A General Theory Based on a Weak Directional Constraint Qualification, SIAM Journal on Control and Optimization, vol.34, issue.4, pp.1151-1171, 1996. ,
DOI : 10.1137/S0363012994267273
URL : https://hal.archives-ouvertes.fr/inria-00074647
Second-Order Necessary Conditions in Pontryagin Form for Optimal Control Problems, SIAM Journal on Control and Optimization, vol.52, issue.6, 2013. ,
DOI : 10.1137/130923452
URL : https://hal.archives-ouvertes.fr/hal-00825273
Second-order sufficient conditions for strong solutions to optimal control problems, Inria Research Report RR, vol.3807, 2013. ,
URL : https://hal.archives-ouvertes.fr/hal-00825260
No-gap second-order optimality conditions for optimal control problems with a single state constraint and control, Mathematical Programming, vol.32, issue.4, pp.21-50, 2009. ,
DOI : 10.1007/s10107-007-0167-8
URL : https://hal.archives-ouvertes.fr/inria-00070189
Second-order analysis for optimal control problems with pure state constraints and mixed control-state constraints, Annales de l'Institut Henri Poincare (C) Non Linear Analysis, vol.26, issue.2, pp.561-598, 2009. ,
DOI : 10.1016/j.anihpc.2007.12.002
URL : https://hal.archives-ouvertes.fr/hal-00778357
Osmolovski? ?. Second-order analysis of optimal control problems with control and initial-final state constraints, J. Convex Anal, vol.17, pp.3-4885, 2010. ,
Sensitivity analysis for relaxed optimal control problems with final-state constraints. Nonlinear Analysis: Theory, Methods & Applications, pp.55-80, 2013. ,
URL : https://hal.archives-ouvertes.fr/hal-00702246
Optimization Problems with Perturbations: A Guided Tour, SIAM Review, vol.40, issue.2, pp.228-264, 1998. ,
DOI : 10.1137/S0036144596302644
URL : https://hal.archives-ouvertes.fr/inria-00073819
Perturbation analysis of optimization problems. Springer Series in Operations Research, 2000. ,
Sur les multi-applications mesurables, Revue fran??aise d'informatique et de recherche op??rationnelle, vol.1, issue.1, pp.91-126, 1967. ,
DOI : 10.1051/m2an/1967010100911
Young measures on topological spaces, volume 571 of Mathematics and its Applications, 2004. ,
Convex analysis and measurable multifunctions, Lecture Notes in Mathematics, vol.580, 1977. ,
DOI : 10.1007/BFb0087685
Metric regularity, tangent sets, and second-order optimality conditions, Applied Mathematics & Optimization, vol.25, issue.1, pp.265-287, 1990. ,
DOI : 10.1007/BF01445166
Maximum principle for the general optimal control problem with phase and regular mixed constraints, Computational Mathematics and Modeling, vol.2, issue.3, pp.364-377, 1993. ,
DOI : 10.1007/BF01128760
Approximation theorem for a nonlinear control system with sliding modes, Proceedings of the Steklov Institute of Mathematics, vol.256, issue.1, pp.102-114, 2007. ,
DOI : 10.1134/S0081543807010063
Jacobi type conditions for singular extremals, Control Cybernet, vol.37, issue.2, pp.285-306, 2008. ,
Implicit functions and solution mappings, 2009. ,
Dubovicki? ? and A. A. Miljutin. Extremal problems with constraints ,
Dubovicki? ? and A. A. Miljutin. Necessary conditions for a weak extremum in optimal control problems with mixed constraints of inequality type ,
Convex analysis and variational problems, Translated from the French, Studies in Mathematics and its Applications, 1976. ,
DOI : 10.1137/1.9781611971088
Optimizing nuclear power plant refueling with mixed-integer programming, European Journal of Operational Research, vol.97, issue.2, pp.269-280, 1997. ,
DOI : 10.1016/S0377-2217(96)00197-X
Relaxation of Control Systems Under State Constraints, SIAM Journal on Control and Optimization, vol.37, issue.4, pp.1291-1309, 1999. ,
DOI : 10.1137/S0363012997331019
On sliding optimal states, Dokl. Akad. Nauk SSSR, vol.143, pp.1243-1245, 1962. ,
Principles of optimal control theory Translated from the Russian by Karol Malowski, Mathematical Concepts and Methods in Science and Engineering, vol.7, 1978. ,
Optimal Control of ODEs and DAEs. De Gruyter Textbook, 2012. ,
URL : https://hal.archives-ouvertes.fr/hal-00724908
Theory of convex programming, Translated from the Russian by K. Makowski, Translations of Mathematical Monographs, vol.36, 1972. ,
A Survey of the Maximum Principles for Optimal Control Problems with State Constraints, SIAM Review, vol.37, issue.2, pp.181-218, 1995. ,
DOI : 10.1137/1037043
Stability Analysis of Optimal Control Problems with a Second-Order State Constraint, SIAM Journal on Optimization, vol.20, issue.1, pp.104-129, 2009. ,
DOI : 10.1137/070707993
URL : https://hal.archives-ouvertes.fr/inria-00186968
Calculus of variations and optimal control theory, 1966. ,
Semi-infinite programming: Conditions of optimality and applications, Optimization techniques (Proc. 8th IFIP Conf, pp.1-11, 1977. ,
DOI : 10.1007/BFb0006502
Variational Approach to Second-Order Optimality Conditions for Control Problems with Pure State Constraints, SIAM Journal on Control and Optimization, vol.50, issue.3, pp.1139-1173, 2012. ,
DOI : 10.1137/110828320
URL : https://hal.archives-ouvertes.fr/hal-00800528
Theory of extremal problems, of Studies in Mathematics and its Applications, 1979. ,
An envelope-like effect of infinitely many inequality constraints on second-order necessary conditions for minimization problems, Math. Programming, pp.73-96, 1988. ,
DOI : 10.1007/BF01580754
Modélisation et résolution de systèmes de contraintes : Application auprobì eme de placement des arrêts et de la production des réacteurs nucléaires d'EDF, 2007. ,
When Constraint Programming and Local Search Solve the Scheduling Problem of Electricit?? de France Nuclear Power Plant Outages, Principles and Practice of Constraint Programming -CP 2006, pp.271-283, 2006. ,
DOI : 10.1007/11889205_21
Sur les fonctions-vecteurscompì etement additives, Bull. Acad. Sci. URSS. Sér. Math. [Izvestia Akad. Nauk SSSR], vol.4, pp.465-478, 1940. ,
Second-order conditions in stability analysis for state constrained optimal control, Journal of Global Optimization, vol.5, issue.1-3, pp.161-168, 2008. ,
DOI : 10.1007/s10898-007-9188-3
Sensitivity analysis for optimal control problems subject to higher order state constraints, Annals of Operations Research, vol.101, issue.1/4, pp.43-73, 2001. ,
DOI : 10.1023/A:1010956104457
First and second order sufficient optimality conditions in mathematical programming and optimal control, Mathematical programming at Oberwolfach (Proc. Conf., Math. Forschungsinstitut, Oberwolfach, pp.163-177, 1979. ,
DOI : 10.1007/BFb0120927
Relaxed Controls and Variational Problems, SIAM Journal on Control, vol.5, issue.3, pp.438-485, 1967. ,
DOI : 10.1137/0305027
Calculus of variations and optimal control, volume 180 of Translations of Mathematical Monographs, 1998. ,
Applications to regular and bang-bang control, volume 24 of Advances in Design and Control, Society for Industrial and Applied Mathematics (SIAM), 2012. ,
A practical guide to the solution of real-life optimal control problems, Control and Cybernetics, vol.23, pp.7-60, 1994. ,
The mathematical theory of optimal processes. Translated from the Russian by K. N. Trirogoff, 1962. ,
Challenge ROADEF/EURO 2010: A large-scale energy management problem with varied constraints, 2010. ,
First Order Conditions for General Nonlinear Optimization, SIAM Journal on Applied Mathematics, vol.30, issue.4, pp.597-607, 1976. ,
DOI : 10.1137/0130053
Regularity and Stability for Convex Multivalued Functions, Mathematics of Operations Research, vol.1, issue.2, pp.130-143, 1976. ,
DOI : 10.1287/moor.1.2.130
Integral functionals, normal integrands and measurable selections, Nonlinear operators and the calculus of variations ,
DOI : 10.1090/S0002-9947-1971-0282283-0
Mathematical Control Theory: Deterministic Finite Dimensional Systems, Texts in Applied Mathematics, 1998. ,
Optimality Conditions for a Constrained Control Problem, SIAM Journal on Control and Optimization, vol.34, issue.2, pp.635-659, 1996. ,
DOI : 10.1137/S0363012994260945
Contrôle optimal: théorie et applications, Collection Mathématiques Concrètes. Vuibert, 2005. ,
Multifunctions with convex closed graph, Czechoslovak Math. J, vol.25, issue.1003, pp.438-441, 1975. ,
Young measures, Workshop on Measure Theory and Real Analysis (Italian) (Grado, pp.152-188349, 1989. ,
DOI : 10.1098/rspa.1933.0121
URL : https://hal.archives-ouvertes.fr/hal-00726642
Optimal Control. Modern Birkhäuser classics, 2000. ,
URL : https://hal.archives-ouvertes.fr/inria-00629428
Necessary conditions for minimum in relaxed variational problems, Journal of Mathematical Analysis and Applications, vol.4, issue.1, pp.129-145, 1962. ,
DOI : 10.1016/0022-247X(62)90034-3
Relaxed variational problems, Journal of Mathematical Analysis and Applications, vol.4, issue.1, pp.111-128, 1962. ,
DOI : 10.1016/0022-247X(62)90033-1
Optimal control of differential and functional equations, 1972. ,
Lectures on the calculus of variations and optimal control theory, 1969. ,
Regularity and stability for the mathematical programming problem in Banach spaces, Applied Mathematics & Optimization, vol.13, issue.1, pp.49-62, 1979. ,
DOI : 10.1007/BF01442543
Gradient-based simulation optimization under probability constraints, European Journal of Operational Research, vol.212, issue.2, pp.345-351, 2011. ,
DOI : 10.1016/j.ejor.2011.01.049
URL : https://hal.archives-ouvertes.fr/hal-00676427
Optimal Control and Viscosity Solutions of Hamilton-Jacobi-Bellman Equations. Modern Birkhäuser Classics, 2008. ,
Convergence of approximation schemes for fully nonlinear second order equations, 29th IEEE Conference on Decision and Control, 1990. ,
DOI : 10.1109/CDC.1990.204046
Dynamic Programming, 1957. ,
Numerical Approximation for a Superreplication Problem under Gamma Constraints, SIAM Journal on Numerical Analysis, vol.47, issue.3, pp.2289-2320, 2009. ,
DOI : 10.1137/080725222
URL : https://hal.archives-ouvertes.fr/hal-00278077
A fast algorithm for the two dimensional HJB equation of stochastic control, ESAIM: Mathematical Modelling and Numerical Analysis, vol.38, issue.4, pp.723-735 ,
DOI : 10.1051/m2an:2004034
URL : https://hal.archives-ouvertes.fr/hal-00988282
Consistency of Generalized Finite Difference Schemes for the Stochastic HJB Equation, SIAM Journal on Numerical Analysis, vol.41, issue.3, pp.1008-1021, 2003. ,
DOI : 10.1137/S0036142901387336
URL : https://hal.archives-ouvertes.fr/inria-00072460
Portfolio management under risk constraints. Lecture notes, 2010. ,
Optimal Control under Stochastic Target Constraints, SIAM Journal on Control and Optimization, vol.48, issue.5, pp.3501-3531, 2010. ,
DOI : 10.1137/090757629
URL : https://hal.archives-ouvertes.fr/hal-00373306
Stochastic Target Problems with Controlled Loss, SIAM Journal on Control and Optimization, vol.48, issue.5, pp.3123-3150, 2010. ,
DOI : 10.1137/08073593X
URL : https://hal.archives-ouvertes.fr/hal-00323383
Super-replication of European options with a derivative asset under constrained finite variation strategies ,
URL : https://hal.archives-ouvertes.fr/hal-00012183
Dynamic consistency for stochastic optimal control problems, Annals of Operations Research, vol.7, issue.1, pp.247-263, 2012. ,
DOI : 10.1007/s10479-011-1027-8
URL : https://hal.archives-ouvertes.fr/hal-00483811
Some properties of viscosity solutions of Hamilton-Jacobi equations, Transactions of the American Mathematical Society, vol.282, issue.2, 1984. ,
DOI : 10.1090/S0002-9947-1984-0732102-X
user's guide to viscosity solutions\\ of second order\\ partial
differential equations, Bulletin of the American Mathematical Society, vol.27, issue.1, pp.1-67, 1992. ,
DOI : 10.1090/S0273-0979-1992-00266-5
Viscosity solutions of hamilton-jacobi equations. Transactions of the, pp.1-42, 1983. ,
Résolution de grandsprobì emes en optimisation stochastique dynamique et synthèse de lois de commande, 2010. ,
Optimisation de lois de gestion energétique des véhicules hybrides, 2012. ,
On the Connectedness of Probabilistic Constraint Sets, Journal of Optimization Theory and Applications, vol.3, issue.3, pp.657-663, 2002. ,
DOI : 10.1023/A:1017976418636
Introduction to chance-constrained programming, 2004. ,
Convexity of chance constraints with independent random variables, Computational Optimization and Applications, vol.9, issue.2, 2007. ,
DOI : 10.1007/s10589-007-9105-1
Convex Analysis and Minimization Algorithms: Part 2: Advanced Theory and Bundle Methods. Convex Analysis and Minimization Algorithms, 1993. ,
DOI : 10.1007/978-3-662-02796-7
Numerical Methods for Stochastic Control Problems in Continuous Time, SIAM Journal on Control and Optimization, vol.28, issue.5, pp.999-1048, 1990. ,
DOI : 10.1137/0328056
Numerical Methods for Stochastic Control Problems in Continuous Time. Applications of mathematics, 2001. ,
Optimum consumption and portfolio rules in a continuous-time model, Journal of Economic Theory, vol.3, issue.4, pp.373-413, 1971. ,
DOI : 10.1016/0022-0531(71)90038-X
Continuous-time stochastic control and optimization with financial applications , volume 61 of Stochastic Modelling and Applied Probability, 2009. ,
Convex Analysis. Princeton mathematical series, 1970. ,
Lectures on Stochastic Programming: Modeling and Theory. MPS-SIAM series on optimization, Society for Industrial and Applied Mathematics, 2009. ,
DOI : 10.1137/1.9780898718751
Optimal Stochastic Control, Stochastic Target Problems, and Backward SDE. Fields Institute Monographs, 2012. ,
Optimal asset allocation in asset liability management. Working Paper 12970, National Bureau of Economic Research, 2007. ,