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Publications of Marianne Akian



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PHD thesis and HDR memoir :

  • 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.



  • Journal  articles:

  • 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. Abstract. Preliminary version in postscript form.


  • 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.


  • 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. Preliminary version in the INRIA research report 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. Preliminary version in the INRIA research report 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. Abstract.


  • 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. Preliminary version in the INRIA research report 4273, Oct. 2001, and in 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. Preliminary version in postscript form.


  • 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. Preliminary version in the INRIA research report 5120, Feb. 04, and in 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. Preliminary version in 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. Preliminary version in 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. Documenta Mathematica, 14, 2009, 195--240. Preliminary version in the INRIA research report 5429 and arXiv:math.MG/0412408.


  • M. Akian, S. Gaubert, and B. Lemmens. Stability and convergence in discrete convex monotone dynamical systems. Journal of Fixed Point Theory and Applications, 9(2), 2011, 295--325. Preliminary version in arXiv:1003.5346.


  • M. Akian, S. Gaubert, V. Nitica, and I. Singer. Best approximation in max-plus semimodules. Linear Algebra and its Applications, 435(12), 2011, 3261--3296. Preliminary version in arXiv:1012.5492.


  • M. Akian, S. Gaubert, and A. Guterman. Tropical polyhedra are equivalent to mean payoff games. Internat. J. Algebra Comput., 22(1), 2012, 1250001, 43. Preliminary version in arXiv:0912.2462.


  • M. Akian and S. Detournay. Multigrid methods for two-player zero-sum stochastic games. Numer. Linear Algebra Appl., 19(2), 2012, 313--342. Preliminary version in arXiv:1107.1653.


  • O. Fercoq, M. Akian, M. Bouhtou, and S. Gaubert. Ergodic control and polyhedral approaches to pagerank optimization. IEEE TAC, 58(1), 2013, 134--148. Preliminary version in arXiv:1011.2348.


  • M. Akian, S. Gaubert, and A. Marchesini. Tropical bounds for eigenvalues of matrices. Linear Algebra and its Applications, 446, 2014, 281--303. Journal article. Preliminary version in arXiv:1309.7319.


  • M. Akian, S. Gaubert, and A. Hochart. Ergodicity conditions for zero-sum games. Discrete and Continuous Dynamical Systems - Series A, 35(9):31, 2015. Preliminary version in arXiv:1405.4658.


  • M. Akian, S. Gaubert, and R. Nussbaum. Uniqueness of the fixed point of nonexpansive semidifferentiable maps. Transactions of the American Mathematical Society, 368(2), 2016. Preliminary version in arXiv:1201.1536.


  • M. Akian, S. Gaubert, and R. Bapat. Non-archimedean valuations of eigenvalues of matrix polynomials. Linear Algebra and its Applications, 498:592--627, 2016. Preliminary version in arXiv:1601.00438.


  • M. Akian, S. Gaubert, and M. Sharify. Log-majorization of the moduli of the eigenvalues of a matrix polynomial by tropical roots. Linear Algebra and its Applications, 2017. Preliminary version in arXiv:1304.2967.


  • M. Akian, S. Gaubert, and A. Hochart. Minimax representation of nonexpansive functions and application to zero-sum recursive games. arXiv:1605.04518, 2016. To appear in Journal of Convex Analysis.



  • Articles published in books or book chapters:

  • 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. Preliminary version in the INRIA reseach report 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.). Series Contemporary Mathematics, Vol. 377, American Mathematical Society. Providence, RI, 2005. pp. 19--51. Preliminary version in ESI Preprint 1447 and in 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.). Series Contemporary Mathematics, Vol. 377, American Mathematical Society. Providence, RI, 2005. pp. 53--77. Preliminary version in ESI Preprint 1485 and in arXiv:math.SP/0405225.


  • M. Akian, R. Bapat, and S. Gaubert. Max-plus algebras. In 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.). Series Contemporary Mathematics. Vol. 495, American Mathematical Society. Providence, RI, 2009. pp. 1--38. Preliminary version in 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.). Series Contemporary Mathematics. Vol. 495, American Mathematical Society. Providence, RI, 2009. pp. 39--60. Preliminary version in arXiv:0812.4866.


  • M. Akian, S. Gaubert, and A. Guterman. Tropical Cramer determinants revisited. In Tropical and Idempotent Mathematics and Applications (G.L. Litvinov and S.N. Sergeev, eds.). Series Contemporary Mathematics. Vol. 616, American Mathematical Society. Providence, RI, 2014. Preliminary version in arXiv:1309.6298, 2013.



  • International conference proceedings:

  • 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. Preliminary version in the INRIA research report 5163 and in 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, Spain, 2005. Preliminary version in 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, Spain, 2005. Preliminary version in 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. Preliminary version in 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.


  • M. Akian, S. Gaubert, and A. Guterman. The correspondence between tropical convexity and mean payoff games. In Proceedings of the 19th International Symposium on Mathematical Theory of Networks and Systems (MTNS 2010), 5­9 July, 2010, Budapest, Hungary, pp. 1295--1302, 2010.


  • M. Akian. Fixed points of discrete convex monotone dynamical systems. In Tropical and Indempotent Mathematics (G.L. Litvinov, V.P. Maslov, A.G. Kushner, and S.N. Sergeev, eds), Moscow, Russia, August 2012.


  • M. Akian, J. Cochet-Terrasson, S. Detournay, and S. Gaubert. Solving multichain stochastic games with mean payoff by policy iteration. In Proc. of the 52nd IEEE Conference on Decision and Control (CDC'13), Florence, Italy, 2013.


  • M. Akian, S. Gaubert, and A. Hochart. Generic uniqueness of the bias vector of mean payoff zero-sum games. In 53rd IEEE Conference on Decision and Control, Los Angeles, 2014. Preliminary version in arXiv:1411.1211.


  • M. Akian, S. Gaubert, and A. Hochart. Hypergraph conditions for the solvability of the ergodic equation for zero-sum games. In 54th IEEE Conference on Decision and Control (CDC 2015), Osaka, 2015. Preliminary version in arXiv:1510.05396.


  • M. Akian and E. Fodjo. Solving Hamilton-Jacobi-Bellman equations by combining a max-plus linear approximation and a probabilistic numerical method. In 22nd International Symposium on Mathematical Theory of Networks and Systems (MTNS), Minneapolis, US, 2016.


  • M. Akian and E. Fodjo. A probabilistic max-plus numerical method for solving stochastic control problems. In 55th Conference on Decision and Control (CDC 2016), Las Vegas, US, 2016. Preliminary version in arXiv:1605.02816.



  • Some unpublished or submitted articles:

  • M. Akian, Theory of cost measures : convergence of decision variables. INRIA research report 2611, 1995.


  • M. Akian, On the continuity of the Cramer transform. INRIA research report 2841, 1996.


  • M. Akian, R. Bapat, and S. Gaubert. Min-plus methods in eigenvalue perturbation theory and generalised Lidskii-Vishik-Ljusternik theorem. arXiv:math.SP/0402090, 2004. Preliminary version in the INRIA research report 5104.


  • M. Akian, S. Gaubert, N. Ninove, Multiple equilibria of nonhomogeneous Markov chains and self-validating Web rankings. arXiv:0712.0469, 2007.


  • M. Akian, S. Gaubert, and R.D. Nussbaum. A Collatz-Wielandt characterization of the spectral radius of order-preserving homogeneous maps on cones. arXiv:1112.5968, 2011.


  • M. Akian, J. Cochet-Terrasson, S. Detournay, and S. Gaubert. Policy iteration algorithm for zero-sum multichain stochastic games with mean payoff and perfect information. arXiv:1208.0446, 2012.


  • M. Akian and S. Gaubert. Policy iteration for perfect information stochastic mean payoff games with bounded first return times is strongly polynomial. arXiv:1310.4953, 2013.


  • M. Akian, S. Gaubert, and A. Hochart. Generic uniqueness of the bias vector of finite stochastic games with perfect information. arXiv:1610.09651, 2016.


  • M. Akian, S. Gaubert, and A. Niv. Tropical compound matrix identities. arXiv:1702.00980, 2017.



  • Max Plus1
    Collective name given to a working group in Discrete Event Systems at INRIA (Méta2 project) composed, at the time of the article, of M. Akian, G. Cohen, S. Gaubert, R. Nikhoukhah and 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 or Max Plus3
    Currently comprising: M. Akian, G. Cohen, S. Gaubert, J.P. Quadrat and M. Viot





    Akian Marianne 2017-02-16