Infinite Dimensional Analysis. A Hitchiker's Guide, 1999. ,
Convergence Speed of Unsteady Distributed Consensus: Decay Estimate Along the Settling Spanning-Trees, SIAM Journal on Control and Optimization, vol.48, issue.1, pp.1-32, 2009. ,
DOI : 10.1137/060673527
URL : https://hal.archives-ouvertes.fr/hal-00793004
A Shooting Algorithm for Optimal Control Problems with Singular Arcs, Journal of Optimization Theory and Applications, vol.16, issue.4, 2011. ,
DOI : 10.1007/s10957-012-0254-8
Geometrical significance of Löwner-Heinz inequality, Proc. Amer, pp.1031-1037, 2000. ,
The Max-Plus Finite Element Method for Solving Deterministic Optimal Control Problems: Basic Properties and Convergence Analysis, SIAM Journal on Control and Optimization, vol.47, issue.2 ,
DOI : 10.1137/060655286
URL : https://hal.archives-ouvertes.fr/inria-00071395
Nonlinear H ? -control, Hamiltonian systems and Hamilton-Jacobi equations, 2011. ,
Duality between probability and optimization, In Idempotency (Bristol Publ. Newton Inst, vol.11, pp.331-353, 1994. ,
DOI : 10.1017/CBO9780511662508.020
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.32.7099
Discrete-time indefinite LQ control with state and control dependent noises, Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228), pp.1249-1250, 2001. ,
DOI : 10.1109/CDC.2001.981058
On the Theory of Dynamic Programming, Proceedings of the National Academy of Sciences, vol.38, issue.8, pp.716-719, 1952. ,
DOI : 10.1073/pnas.38.8.716
Dynamic programming, 1957. ,
Approximate policy iteration: a survey and some new methods, Journal of Control Theory and Applications, vol.27, issue.3, pp.310-335, 2011. ,
DOI : 10.1007/s11768-011-1005-3
Practical methods for optimal control using nonlinear programming, volume 3 of Advances in Design and Control, Society for Industrial and Applied Mathematics (SIAM), 2001. ,
Randomized gossip algorithms, IEEE Transactions on Information Theory, vol.52, issue.6, pp.2508-2530, 2006. ,
DOI : 10.1109/TIT.2006.874516
On the exponential metric increasing property, Linear Algebra and its Applications, vol.375, pp.211-220, 2003. ,
DOI : 10.1016/S0024-3795(03)00647-5
Extensions of Jentzsch's theorem, Trans. Amer. Math. Soc, vol.85, pp.219-227, 1957. ,
Bocop -A collection of examples, 2012. ,
URL : https://hal.archives-ouvertes.fr/hal-00726992
Approximation of General Smooth Convex Bodies, Advances in Mathematics, vol.153, issue.2, pp.325-341, 2000. ,
DOI : 10.1006/aima.1999.1904
Kalman Filtering with Random Coefficients and Contractions, SIAM Journal on Control and Optimization, vol.31, issue.4, pp.942-959, 1993. ,
DOI : 10.1137/0331041
A relaxation method of finding a common point of convex sets and its application to the solution of problems in convex programming, Z. Vy?isl. Mat. i Mat ,
On a characterization of flow-invariant sets, Communications on Pure and Applied Mathematics, vol.23, issue.2, pp.261-263, 1970. ,
DOI : 10.1002/cpa.3160230211
On the complexity of computing zero-error and holevo capacity of quantum channels. arxiv:0709, 2008. ,
Parallel and distributed computation: numerical methods, 1989. ,
Robust optimization, Princeton Series in Applied Mathematics, 2009. ,
DOI : 10.1515/9781400831050
Hilbert's metric and positive contraction mappings in a Banach space, Arch. Rational Mech. Anal, vol.52, pp.330-338, 1973. ,
Convex optimization, 2004. ,
Q-learning and enhanced policy iteration in discounted dynamic programming, Math. Oper. Res, vol.37, issue.1, pp.66-94, 2012. ,
Anti-Dissipative Schemes for Advection and Application to Hamilton???Jacobi???Bellmann Equations, Journal of Scientific Computing, vol.21, issue.5, pp.1-33, 2007. ,
DOI : 10.1007/s10915-005-9017-0
URL : https://hal.archives-ouvertes.fr/hal-00878221
A Patchy Dynamic Programming Scheme for a Class of Hamilton--Jacobi--Bellman Equations, SIAM Journal on Scientific Computing, vol.34, issue.5, pp.2625-2649, 2012. ,
DOI : 10.1137/110841576
URL : https://hal.archives-ouvertes.fr/inria-00628108
On a discrete approximation of the Hamilton-Jacobi equation of dynamic programming, Applied Mathematics & Optimization, vol.8, issue.1, pp.367-377, 1983. ,
DOI : 10.1007/BF01448394
An efficient algorithm for Hamilton???Jacobi equations in high dimension, Computing and Visualization in Science, vol.97, issue.1, pp.15-29, 2004. ,
DOI : 10.1007/s00791-004-0124-5
A domain decomposition method for Bellman equations, Domain decomposition methods in scientific and engineering computing, pp.477-483, 1993. ,
DOI : 10.1090/conm/180/02008
Duality and separation theorems in idempotent semimodules, Linear Algebra and its Applications, vol.379, pp.395-422, 2004. ,
DOI : 10.1016/j.laa.2003.08.010
URL : https://hal.archives-ouvertes.fr/inria-00071917
Viscosity solutions of Hamilton-Jacobi equations, Trans. Amer. Math. Soc, vol.277, issue.1, pp.1-42, 1983. ,
Two approximations of solutions of Hamilton-Jacobi equations, Mathematics of Computation, vol.43, issue.167, pp.1-19, 1984. ,
DOI : 10.1090/S0025-5718-1984-0744921-8
Generalized gradients and applications, Trans. Amer. Math. Soc, vol.205, pp.247-262, 1975. ,
Nonsmooth analysis and control theory, 1998. ,
URL : https://hal.archives-ouvertes.fr/hal-00863298
Incremental pruning: A simple, fast, exact method for partially observable markov decision processes Stochastic linear quadratic regulators with indefinite control weight costs, Proceedings of the Thirteenth Conference on Uncertainty in Artificial Intelligence, pp.54-611685, 1997. ,
A course in functional analysis, volume 96 of Graduate Texts in Mathematics, 1990. ,
Replacing continuous demand with discrete demand in a competitive location model, Naval Research Logistics, vol.44, issue.1, pp.81-95, 1997. ,
DOI : 10.1002/(SICI)1520-6750(199702)44:1<81::AID-NAV5>3.0.CO;2-I
A max-plus based fundamental solution for a class of infinite dimensional Riccati equations, IEEE Conference on Decision and Control and European Control Conference, pp.615-620, 2011. ,
DOI : 10.1109/CDC.2011.6161017
Central limit theorem for non-stationary Markov chains. I. Teor, Veroyatnost . i Primenen, vol.1, pp.72-89, 1956. ,
Comparison theorems and non-oscillation for differential equations in a B???-algebra, Nonlinear Analysis: Theory, Methods & Applications, vol.6, issue.1, pp.21-33, 1982. ,
DOI : 10.1016/0362-546X(82)90099-2
An elementary proof of the Birkhoff-Hopf theorem, Math. Proc. Cambridge Philos. Soc, vol.117, issue.1, pp.31-55, 1995. ,
A numerical approach to the infinite horizon problem of deterministic control theory, Appl. Math. Optim. Corrigenda in Appl. Math. Optim, vol.15, issue.23, pp.1-13213, 1987. ,
Irreducible positive linear maps on operator algebras, Proc. Amer, pp.3381-3390, 1996. ,
Nonconvex quadratic programming, semidefinite relaxations and randomization algorithms in information and decision systems In System theory: modeling, analysis and control, Kluwer Internat. Ser. Engrg . Comput. Sci, vol.518, pp.255-274, 1999. ,
Discrete time high-order schemes for viscosity solutions of Hamilton-Jacobi-Bellman equations, Numerische Mathematik, vol.67, issue.3, pp.315-344, 1994. ,
DOI : 10.1007/s002110050031
Functional analysis and infinite-dimensional geometry, CMS Books in Mathematics, vol.8, 2001. ,
A splitting algorithm for Hamilton-Jacobi-Bellman equations, Applied Numerical Mathematics, vol.15, issue.2, pp.207-218, 1992. ,
DOI : 10.1016/0168-9274(94)00017-4
A Max-Plus-Based Algorithm for a Hamilton--Jacobi--Bellman Equation of Nonlinear Filtering, SIAM Journal on Control and Optimization, vol.38, issue.3, pp.683-710, 2000. ,
DOI : 10.1137/S0363012998332433
Real analysis, Modern techniques and their applications, 1999. ,
Deterministic and stochastic optimal control, Applications of Mathematics, issue.1, 1975. ,
The Perron-Frobenius theorem for homogeneous, monotone functions, Transactions of the American Mathematical Society, vol.356, issue.12, pp.4931-4950, 2004. ,
DOI : 10.1090/S0002-9947-04-03470-1
Curse of dimensionality reduction in max-plus based approximation methods: Theoretical estimates and improved pruning algorithms, IEEE Conference on Decision and Control and European Control Conference, pp.1054-1061, 2011. ,
DOI : 10.1109/CDC.2011.6161386
URL : https://hal.archives-ouvertes.fr/hal-00935266
User's guide for NPSOL (version 4.0): A Fortran package for nonlinear programming, 94305, 1986. ,
The contraction rate in thompson metric of order-preserving flows on a cone with application to generalized Riccati equations, 2012. ,
Dobrushin ergodicity coefficient for markov operators on cones, and beyond. arxiv:1302, 2012. ,
URL : https://hal.archives-ouvertes.fr/hal-00935284
Markov operators on cones and noncommutative consensus, Proceedings of the European Control Conference ECC 2013, pp.2693-2700 ,
URL : https://hal.archives-ouvertes.fr/hal-00935312
Asymptotic estimates for best and stepwise approximation of convex bodies, I. Forum Math, vol.5, issue.5, pp.281-297, 1993. ,
Asymptotic estimates for best and stepwise approximation of convex bodies, II. Forum Math, vol.5, issue.6, pp.521-538, 1993. ,
Convex and discrete geometry, 2007. ,
Convergent activation dynamics in continuous time networks, Neural Networks, vol.2, issue.5, pp.331-349, 1989. ,
DOI : 10.1016/0893-6080(89)90018-X
Ausfüllung und überdeckung konvexer Körper durch konvexe Körper, Monatsh. Math, vol.53, pp.81-131, 1949. ,
An inequality for positive linear integral operators, Journal of Mathematics and Mechanics, vol.12, issue.5, pp.683-692, 1963. ,
A Discontinuous Galerkin Finite Element Method for Hamilton--Jacobi Equations, SIAM Journal on Scientific Computing, vol.21, issue.2, pp.666-690, 1999. ,
DOI : 10.1137/S1064827598337282
Monotone dynamical systems In Handbook of differential equations: ordinary differential equations, pp.239-357, 2005. ,
Idempotent analysis and its applications, volume 401 of Mathematics and its Applications Translation of Idempotent analysis and its application in optimal control (Russian), " Nauka " Moscow, 1994. ,
The Contraction Mapping Approach to the Perron-Frobenius Theory: Why Hilbert's Metric?, Mathematics of Operations Research, vol.7, issue.2, pp.198-210, 1982. ,
DOI : 10.1287/moor.7.2.198
On Converting Optimal Control Problems into Nonlinear Programming Problems, Computational mathematical programming, pp.261-280, 1984. ,
DOI : 10.1007/978-3-642-82450-0_9
Méthode des éléments finis max-plus pour la résolution numérique de problèmes de commande optimale déterministe, 2007. ,
Convex analysis on the Hermitian matrices, SIAM J. Optim, vol.6, issue.1, pp.164-177, 1996. ,
Analysis of a classification-based policy iteration algorithm, ICML, pp.607-614, 2010. ,
URL : https://hal.archives-ouvertes.fr/inria-00482065
Viscosity solutions of fully nonlinear second order equations and optimal stochastic control in infinite dimensions. II. Optimal control of Zakai's equation, Stochastic partial differential equations and applications, pp.147-170, 1988. ,
A Birkhoff Contraction Formula with Applications to Riccati Equations, SIAM Journal on Control and Optimization, vol.46, issue.3, pp.930-951, 2007. ,
DOI : 10.1137/050637637
Invariant metrics, contractions and nonlinear matrix equations, Nonlinearity, vol.21, issue.4, pp.857-878, 2008. ,
DOI : 10.1088/0951-7715/21/4/011
Idempotent functional analysis: an algebraic approach, Mathematical Notes, vol.69, issue.5/6, pp.696-729, 2001. ,
DOI : 10.1023/A:1010266012029
Markov chains and mixing times, 2009. ,
The simplest proof of Burnside's theorem on matrix algebras, Linear Algebra and its Applications, vol.383, pp.45-47, 2004. ,
DOI : 10.1016/j.laa.2003.08.012
Differential Games, Optimal Control and Directional Derivatives of Viscosity Solutions of Bellman???s and Isaacs??? Equations, SIAM Journal on Control and Optimization, vol.23, issue.4, pp.566-583, 1985. ,
DOI : 10.1137/0323036
Asymptotic approximation of smooth convex bodies by general polytopes, Mathematika, vol.127, issue.01, pp.103-125, 1999. ,
DOI : 10.1016/0022-247X(75)90125-0
e-approximations with minimum packing constraint violation, Proceedings of the twenty-fourth annual ACM symposium on Theory of computing, STOC '92, pp.771-782, 1992. ,
Generalization of the Hilbert metric to the space of positive definite matrices, Pacific Journal of Mathematics, vol.166, issue.2, pp.339-355, 1994. ,
DOI : 10.2140/pjm.1994.166.339
Quantum zero-error capacity, Int. J. Quanum Inform, vol.03, p.135, 2005. ,
Differential equations on closed subsets of a Banach space, Trans ,
Numerical solution of singular control problems using multiple shooting techniques, J. of Optimization Theory and Applications, vol.18, pp.235-257, 1976. ,
A uniqueness result for the Isaacs equation corresponding to nonlinear H ? control, Math. Control Signals Systems, vol.11, issue.4, pp.303-334, 1998. ,
Max-plus methods for nonlinear control and estimation. Systems & Control: Foundations & Applications, Birkhäuser Boston Inc, 2006. ,
A curse-of-dimensionality-free numerical method for solution of certain HJB PDEs, SIAM J. Control Optim, vol.46, issue.4, pp.1239-1276, 2007. ,
Convergence rate for a curse-of-dimensionality-free method for Hamilton-Jacobi-Bellman PDEs represented as maxima of quadratic forms, SIAM J. Control Optim, vol.48, issue.4, pp.2651-2685, 2009. ,
A Lower Bound on Convergence of a Distributed Network Consensus Algorithm, Proceedings of the 44th IEEE Conference on Decision and Control, pp.2356-2361, 2005. ,
DOI : 10.1109/CDC.2005.1582514
Curse-of-complexity attenuation in the curse-of-dimensionality-free method for HJB PDEs, 2008 American Control Conference, pp.4684-4690, 2008. ,
DOI : 10.1109/ACC.2008.4587234
Matrix analysis and applied linear algebra With 1 CD-ROM (Windows, Macintosh and UNIX) and a solutions manual, Society for Industrial and Applied Mathematics (SIAM), 2000. ,
Convergence rate for a curseof-dimensionality-free method for a class of HJB PDEs, SIAM J. Control Optim, vol.48, issue.5, pp.3052-3079, 2009. ,
Stability of multiagent systems with time-dependent communication links, IEEE Transactions on Automatic Control, vol.50, issue.2, pp.169-182, 2005. ,
DOI : 10.1109/TAC.2004.841888
Least squares policy evaluation algorithms with linear function approximation, Discrete Event Dynamic Systems, vol.13, issue.1/2, pp.79-110, 2003. ,
DOI : 10.1023/A:1022192903948
Quantum computation and quantum information, 2000. ,
Patchy Solutions of Hamilton-Jacobi-Bellman Partial Differential Equations, In Modeling, estimation and control Lecture Notes in Control and Inform. Sci, vol.364, pp.251-270, 2007. ,
DOI : 10.1007/978-3-540-73570-0_20
Hilbert's projective metric and iterated nonlinear maps, Mem. Amer. Math. Soc, issue.391, pp.75-137, 1988. ,
Finsler structures for the part metric and Hilbert's projective metric and applications to ordinary differential equations, Differential Integral Equations, vol.7, issue.5-6, pp.1649-1707, 1994. ,
An analysis of approximations for maximizing submodular set functions???I, Mathematical Programming, vol.16, issue.1, pp.265-294, 1978. ,
DOI : 10.1007/BF01588971
Spatial tessellations: concepts and applications of Voronoi diagrams Wiley Series in Probability and Statistics, 2000. ,
Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations, Journal of Computational Physics, vol.79, issue.1, pp.12-49, 1988. ,
DOI : 10.1016/0021-9991(88)90002-2
High-Order Essentially Nonoscillatory Schemes for Hamilton???Jacobi Equations, SIAM Journal on Numerical Analysis, vol.28, issue.4, pp.907-922, 1991. ,
DOI : 10.1137/0728049
Convergence Speed in Distributed Consensus and Averaging, SIAM Journal on Control and Optimization, vol.48, issue.1, pp.33-55, 2009. ,
DOI : 10.1137/060678324
The mathematical theory of optimal processes. Translated from the Russian by K. N. Trirogoff, 1962. ,
Contraction of Riccati flows applied to the convergence analysis of a maxplus curse of dimensionality free method. arxiv:1301, p.4777, 2013. ,
URL : https://hal.archives-ouvertes.fr/hal-00935300
Contraction of Riccati Flows Applied to the Convergence Analysis of a Max-Plus Curse-of-Dimensionality--Free Method, Proceedings of the European Control Conference ECC 2013 ,
DOI : 10.1137/130906702
URL : https://hal.archives-ouvertes.fr/hal-00935300
Solvability and asymptotic behavior of generalized Riccati equations arising in indefinite stochastic LQ controls, IEEE Transactions on Automatic Control, vol.46, issue.3, pp.428-440, 2001. ,
DOI : 10.1109/9.911419
The theorems of Bony and Brezis on flow-invariant sets, Amer. Math. Monthly, vol.79, pp.740-747, 1972. ,
Riccati differential equations, Mathematics in Science and Engineering, vol.86, 1972. ,
Hilbert's projective metric in quantum information theory, Journal of Mathematical Physics, vol.52, issue.8, p.82201, 2011. ,
DOI : 10.1063/1.3615729
Convex analysis, Princeton Mathematical Series, issue.28, 1970. ,
Packing and covering, Cambridge Tracts in Mathematics and Mathematical Physics, issue.54, 1964. ,
Variational analysis, of Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences, 1998. ,
DOI : 10.1007/978-3-642-02431-3
Linear matrix inequalities, Riccati equations, and indefinite stochastic linear quadratic controls, IEEE Transactions on Automatic Control, vol.45, issue.6, pp.1131-1143, 2000. ,
DOI : 10.1109/9.863597
Polyhedral approximation of smooth convex bodies, Journal of Mathematical Analysis and Applications, vol.128, issue.2, pp.470-474, 1987. ,
DOI : 10.1016/0022-247X(87)90197-1
Applications of ergodicity coefficients to homogeneous Markov chains In 50 Years after Doeblin: Developments in the Theory of Markov Chains, Markov Processes and Sums of Random Variables, pp.2-7, 1991. ,
Fast marching methods, SIAM Rev, vol.41, issue.2, pp.199-235, 1999. ,
Reduced-complexity numerical method for optimal gate synthesis, Physical Review A, vol.82, issue.4, p.42319, 2010. ,
DOI : 10.1103/PhysRevA.82.042319
Analysis of stochastic dual dynamic programming method, European Journal of Operational Research, vol.209, issue.1, pp.63-72, 2011. ,
DOI : 10.1016/j.ejor.2010.08.007
Consensus protocols for networks of dynamic agents, Proceedings of the 2003 American Control Conference, 2003., pp.951-956, 2003. ,
DOI : 10.1109/ACC.2003.1239709
$\mathcal{H}_\infty $ Control of Nonlinear Systems: Differential Games and Viscosity Solutions, SIAM Journal on Control and Optimization, vol.34, issue.3, pp.1071-1097, 1996. ,
DOI : 10.1137/S0363012994266413
A Quantum Version of Wielandt's Inequality, IEEE Transactions on Information Theory, vol.56, issue.9, pp.4668-4673, 2010. ,
DOI : 10.1109/TIT.2010.2054552
Deterministic filtering and max-plus methods for robust state estimation in multi-sensor settings. arxiv:1211, 1449. ,
Consensus in noncommutative spaces, Proceedings of the 49th IEEE Conference on Decision and Control, pp.6596-6601, 2010. ,
URL : https://hal.archives-ouvertes.fr/hal-00576914
From kuramoto to crawford: exploring the onset of synchronization in populations of coupled oscillators, Phys. D, pp.1-20, 2000. ,
Ordered upwind methods for static Hamilton-Jacobi equations: theory and algorithms, SIAM J. Numer. Anal, vol.41, issue.1, pp.325-363, 2003. ,
Distributed asynchronous deterministic and stochastic gradient optimization algorithms, IEEE Transactions on Automatic Control, vol.31, issue.9, pp.31803-812, 1986. ,
DOI : 10.1109/TAC.1986.1104412
On certain contraction mappings in a partially ordered vector space, Proc. Amer. Math. soc, vol.14, pp.438-443, 1963. ,
An analysis of temporal-difference learning with function approximation, IEEE Trans. Automat. Control, vol.42, issue.5, pp.674-690, 1997. ,
Approximation algorithms, 2001. ,
Convergence in multiagent coordination, consensus, and flocking, Proceedings of the joint 44th IEEE Conference on Decision and Control and European Control Conference, pp.2996-3000, 2005. ,
Stochastic controls, Applications of Mathematics, vol.43, 1999. ,
DOI : 10.1007/978-1-4612-1466-3
Speeding up the convergence of value iteration in partially observable markov decision processes, Journal of Artificial Intelligence Research, vol.14, 2001. ,