Mes publications

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Thèse et HDR :

M. Akian, Méthodes multigrilles en contrôle stochastique. Thèse de Doctorat. Université Paris IX-Dauphine, 1990.

M. Akian, Algèbre max-plus, applications monotones contractantes et équations aux dérivées partielles : trois approches du contrôle optimal. Habilitation à Diriger des Recherches, Université Pierre et Marie Curie, 2007.

Articles de journaux :

Max Plus¹, L'algèbre (max,+) et sa symétrisation ou l'algèbre des équilibres. C. R. Acad. Sci. Paris, t. 311, Série II, 1990.

M.Akian, J.L. Menaldi, and A.Sulem, Multi-asset portfolio selection problem with transaction costs. Probabilités numériques (Paris, 1992). Mathematics and Computers in Simulation 38, 1995, 163-172.

M.Akian, J.L. Menaldi, and A.Sulem, On an investement-consumption model with transaction costs. SIAM Journal of Control and Optimization 34, no. 1, 1996, 329-364. Résumé. Version préliminaire sous forme postscript.

J.P. Quadrat and Max-Plus Working group², Min-plus linearity and Statistical Mechanics. Markov Processes and Related fields, 3, nb 4, 1997, 565-587. Version préliminaire sous forme pdf.

M. Akian, R. Bapat, and S. Gaubert, Asymptotics of the Perron eigenvalue and eigenvector using max-algebra. C. R. Acad. Sci. Paris, t. 327, Série I, 1998, 927-932. Version préliminaire dans le rapport de recherche INRIA 3450.

M. Akian, Densities of idempotent measures and large deviations . Transactions of the American Mathematical Society, 351, no. 11, 1999, 4515-4543. postscript, pdf.

M. Akian and P.-A. Bliman, On super-high frequencies in discontinuous 1st-order delay-differential equations. Journal of Differential Equations, 162, 2000, 326-358. Version préliminaire dans le rapport de recherche INRIA 3443.

M. Akian, A. Sulem, and M. Taksar, Dynamic optimisation of long term growth rate for a portfolio with transaction costs and logarithmic utility . Mathematical Finance, 11(2), 2001, 153-188. pdf.

M. Akian and S. Bismuth, Instability of rapidly-oscillating periodic solutions for discontinuous differential delay equations. Differential and Integral Equations, 15(1), 2002, 53-90. postscript, pdf.

M. Akian, P.-A. Bliman, and M. Sorine, Control of delay systems with relay. IMA Journal on Mathematical Control and Information, Special issue on Analysis and Design of Delay and Propagation Systems , 19, 2002,133-155. Résumé.

M. Akian, S. Gaubert, and V. Kolokoltsov. Invertibility of Functional Galois Connections. Comptes Rendus Mathématique 335(11), 2002, 883--888. doi:10.1016/S1631-073X(02)02594-3.

M. Akian and S. Gaubert. Spectral theorem for convex monotone homogeneous maps, and ergodic control. Nonlinear Analysis. Theory, Methods & Applications. 52(2), 2003, 637--679. doi:10.1016/S0362-546X(02)00170-0. Version préliminaire dans le rapport de recherche INRIA 4273, Oct. 2001, et dans arXiv:math.SP/0110108.

M. Akian and I. Singer. Topologies on lattice ordered groups, separation from closed downward sets and conjugations of type Lau. Optimization. 52(6), 2003, 629--672. doi:10.1080/02331930310001637396. Version préliminaire sous forme postscript.

M. Akian, R. Bapat, and S. Gaubert. Perturbation of eigenvalues of matrix pencils and optimal assignment problem. Comptes Rendus Mathématique 339, 2004, 103--108. doi:10.1016/j.crma.2004.05.001. Version préliminaire dans le rapport de recherche INRIA 5120, et dans arXiv:math.SP/0402438.

M. Akian, S. Gaubert, B. Lemmens and R. Nussbaum. Iteration of order preserving subhomogeneous maps on a cone. Mathematical Proceedings of the Cambridge Philosophical Society 140(1), 2006, 157-176. doi:10.1017/S0305004105008832. Version préliminaire dans arXiv:math.DS/0410084.

M. Akian, S. Gaubert, and A. Lakhoua. The max-plus finite element method for solving deterministic optimal control problems: basic properties and convergence analysis. SIAM Journal on Control and Optimization, 47, no. 2, 2008, 817--848. Version préliminaire dans arXiv:math.OC/0603619, 2006.

M. Akian, B. David, and S. Gaubert. Un théorème de représentation des solutions de viscosité d'une équation d'Hamilton-Jacobi-Bellman ergodique dégénérée sur le tore. C. R. Acad. Sci. Paris, Ser. I, 346:1149-1154, 2008.

M. Akian, S. Gaubert, and C. Walsh. The max-plus Martin boundary. Accepté pour publication dans Documenta Mathematica. Version préliminaire dans le rapport de recherche INRIA 5429 et arXiv:math.MG/0412408.

M. Akian, S. Gaubert, N. Ninove, Multiple equilibria of nonhomogeneous Markov chains and self-validating Web rankings. 2007. Accepté pour publication dans SIMAX sous réserve de corrections. Version préliminaire dans arXiv:0712.0469.

Articles publiés dans des livres ou chapitres de livres :

M. Akian, Résolution numérique d'équations d'Hamilton-Jacobi-Bellman au moyen d'algorithmes multigrilles et d'itérations sur les politiques. In Analysis and optimisation of systems. Lecture notes in control and information sciences, vol. 111, Springer Verlag, 1988.

M. Akian, Analyse de l'algorithme multigrille FMGH de résolution d'équations d'Hamilton-Jacobi-Bellman. In Analysis and optimisation of systems. Lecture notes in control and information sciences, vol. 144, Springer Verlag, 1990.

M. Akian, J.P. Quadrat, and M. Viot, Bellman processes. In 11th International Conference on Analysis and Optimization of Systems : Discrete Event Systems. Lecture notes in control and information sciences, vol. 199, Springer Verlag, 1994.

S. Gaubert, and Max Plus³, Methods and Applications of (max,+) linear Algebra, In STACS 97 (Lubeck). Lecture Notes in Comput. Sci., vol. 1200, pp. 261--282. Springer, Berlin, 1997. Version préliminaire dans le Rapport de recherche INRIA 3088.

M. Akian, J.P. Quadrat, and M. Viot, Duality between probability and optimization. In Idempotency (J. Gunawardena, ed.). Publication of the Isaac Newton Institute, Crambridge University press, 1998. postscript, pdf.

M. Akian, S. Gaubert, and V. Kolokoltsov. Set coverings and invertibility of Functional Galois Connections. In Idempotent Mathematics and Mathematical Physics (G.L. Litvinov and V.P. Maslov, eds.). Série Contemporary Mathematics, Vol. 377, American Mathematical Society. Providence, RI, 2005. pp. 19--51. Version préliminaire dans l'ESI Preprint 1447 et dans arXiv:math.FA/0403441.

M. Akian, S. Gaubert, and C. Walsh. Discrete max-plus spectral theory. In Idempotent Mathematics and Mathematical Physics (G.L. Litvinov and V.P. Maslov, eds.). Série Contemporary Mathematics, Vol. 377, American Mathematical Society. Providence, RI, 2005. pp. 53--77. Version préliminaire dans l'ESI Preprint 1485 et dans arXiv:math.SP/0405225.

M. Akian, R. Bapat, and S. Gaubert. Max-plus algebras. Dans Handbook of Linear Algebra (Discrete Mathematics and Its Applications, Vol. 39) (L. Hogben, ed.). Chapman & Hall/CRC, 2006.

M. Akian, S. Gaubert, and N. Ninove, The T-PageRank: a model of self-validating effects of web surfing. In Positive Systems. Lecture notes in control and information sciences, vol. 341, Springer Verlag, 2006, pp. 239--246.

M. Akian, S. Gaubert, and A. Guterman. Linear independence over tropical semirings and beyond. In Proceedings of the International Conference on Tropical and Idempotent Mathematics (G.L. Litvinov and S.N. Sergeev, eds.). Série Contemporary Mathematics. American Mathematical Society. Accepté pour publication. Version préliminaire dans arXiv:0812.3496.

M. Akian, S. Gaubert, and V. Kolokoltsov. The optimal assignment problem for a countable state space. In Proceedings of the International Conference on Tropical and Idempotent Mathematics (G.L. Litvinov and S.N. Sergeev, eds.). Série Contemporary Mathematics. American Mathematical Society. Accepté pour publication. Version préliminaire dans arXiv:0812.4866.

Actes de conférences internationales :

M. Akian and A. Bensoussan, On the stochastic Ramsey problem. IEEE CDC, Athènes, Grèce, 1986.

M. Akian, J.P. Chancelier, and J.P. Quadrat, Dynamic programming complexity and application. IEEE CDC, Austin Texas, Dec. 1988.

Max Plus¹, Linear systems in (max, +) algebra. Proceedings of the 29th Conference on Decision and Control, Honolulu, Hawaii, Dec. 1990. postscript, pdf.

M. Akian and A. Sulem, Application of ``Pandore'', an expert system in stochastic control, to portfolio selection problems. In Artificial Intelligence, Expert Systems and Symbolic Computing, North Holand (IMACS), 1992.

Max-Plus Working group³, presented by Jean-Pierre Quadrat, Max-plus algebra and applications to system theory and optimal control. Proceedings of the International Congress of Mathematicians, Zürich, 1994. Birkhäuser, Basel, Switzerland 1995.

M. Akian, P. Séquier, A Sulem, and A. Aboulalaa, A finite horizon portfolio selection problem with multi-risky assets and transaction costs : the dynamic asset allocation example. In Actes Association Française de Finance, Bordeaux, Juin 1995.

M. Akian, P. Séquier, and A Sulem, A finite horizon multidimensional portfolio selection problem with singular transactions. Proceedings of the 34th Conference on Decision and Control, New Orléans, Dec. 1995, vol. 3, 2193-2198. pdf.

M. Akian, A Sulem, and M. Taksar, Maximization of a long term growth rate for a mixed portfolio with transaction costs. Proceedings of the 17th IFIP Conference, Prague, Juillet 1995, 132-135.

M. Akian, J.P. Quadrat, and M. Viot, Bellman processes with independent increments. Proceedings of the 17th IFIP Conference, Prague, Juillet 1995, 207-210.

M. Akian and P.-A. Bliman, On super-high-frequencies in discontinuous 1st-order delay-differential equations. In 6th IEEE Mediterranean Conference on Control and Systems, Alghero, Italy, June 9-11, 1998.

M. Akian, P.-A. Bliman, and M. Sorine, P.I. control of nonlinear oscillations for a system with delay. In 8th IFAC LSS'98, Patras, Greece, July 15-17, 1998.

K. Blin, M. Akian, F. Bonnans, E. Hoffman, C. Martini, and K. Zeghal, A stochastic conflict detection model revisited. In Proceedings of AIAA GNC, Denver, August 2000.

K. Blin, M. Akian, F. Bonnans, E. Hoffman, and K. Zeghal, A stochastic conflict detection method integrating planned heading and velocity changes. In Proceedings of the IEEE CDC, Sydney, Dec. 2000.

M. Akian and S. Gaubert, A spectral theorem for convex monotone homogeneous maps. In Proceedings of the Satellite Workshop on Max-Plus Algebras, IFAC SSSC'01, Praha, 2001. Elsevier.

M. Akian, R. B. Bapat, and S. Gaubert, Generic Asymptotics of Eigenvalues using Min-Plus Algebra. In Proceedings of the Satellite Workshop on Max-Plus Algebras, IFAC SSSC'01, Praha, 2001. Elsevier.

M. Akian, S. Gaubert, and A. Lakhoua. A max-plus finite element method for solving finite horizon deterministic optimal control problems. In Proceedings of MTNS 2004. Version préliminaire dans le rapport de recherche INRIA 5163 et dans arXiv:math.OC/0404184, 2004.

M. Akian, S. Gaubert, and A. Lakhoua. The max-plus finite element method for optimal control problems: further approximation results. In Proceedings of the joint 44th IEEE Conference on Decision and Control and European Control Conference ECC 2005 (CDC-ECC'05), Seville, Espagne, 2005. Version préliminaire dans arXiv:math.OC/0509250.

M. Akian, S. Gaubert, and V. N. Kolokoltsov. Solutions of max-plus linear equations and large deviations. In Proceedings of the joint 44th IEEE Conference on Decision and Control and European Control Conference ECC 2005 (CDC-ECC'05), Seville, Espagne, 2005. Version préliminaire dans arXiv:math.PR/0509279.

M. Akian, S. Gaubert, and C. Walsh. How to find horizon-independent optimal strategies leading off to infinity: a max-plus approach. In Proc. of the 45th IEEE Conference on Decision and Control (CDC'06) , San Diego, 2006. Version préliminaire dans arXiv:math.OC/0609243.

M. Akian. Representation of stationnary solutions of Hamilton-Jacobi-Bellman equations: a max-plus point of view. In G .L. Litvinov, V. P. Maslov, and S. N. Sergeev, editors, Proc. of the International Workshop ``Idempotent and Tropical Mathematics and problems of Mathematical Physics'', Moscow, Aug. 25-30, 2007, volume 1, pages 6--11.

M. Akian, S. Gaubert, and A. Lakhoua. Convergence analysis of the max-plus finite element method for solving deterministic optimal control problems. In Proc. of the 47th IEEE Conference on Decision and Control (CDC'08), Cancun, 2008.

Quelques articles soumis :

M. Akian, R. Bapat, and S. Gaubert. Min-plus methods in eigenvalue perturbation theory and generalised Lidskii-Vishik-Ljusternik theorem. Rapport de recherche INRIA 5104 et arXiv:math.SP/0402090, 2004.

Quelques rapports INRIA non publiés :

M. Akian, Theory of cost measures : convergence of decision variables. Rapport de recherche INRIA 2611, 1995.

M. Akian, On the continuity of the Cramer transform. Rapport de recherche INRIA 2841, 1996.

Max Plus¹

Nom collectif donné au groupe de travail en théorie des Systèmes à Evénements Discrets à l'INRIA (Projet Méta2) composé au moment de l'article de M. Akian, G. Cohen, S. Gaubert, R. Nikhoukhah et J.P. Quadrat.

Max-Plus Working group²

Currently comprising: M. Akian, G. Cohen, S. Gaubert, M. Mc Gettrick, J.P. Quadrat and M. Viot

Max-Plus group³ ou Max Plus³

Currently comprising: M. Akian, G. Cohen, S. Gaubert, J.P. Quadrat and M. Viot