Bibliography

Major publications by the team in recent years

• 1M. Akian.
  Densities of idempotent measures and large deviations, in: Transactions of the American Mathematical Society, 1999, vol. 351, n^o 11, pp. 4515–4543.
• 2M. Akian, R. Bapat, S. Gaubert.
  Max-plus algebras, in: Handbook of Linear Algebra (Discrete Mathematics and Its Applications), L. Hogben (editor), Chapman & Hall/CRC, 2006, vol. 39, Chapter 25.
• 3M. Akian, S. Gaubert.
  Spectral Theorem for Convex Monotone Homogeneous Maps, and ergodic Control, in: Nonlinear Analysis. Theory, Methods & Applications, 2003, vol. 52, n^o 2, pp. 637-679.
  http://hal.inria.fr/inria-00000201/en/
• 4M. Akian, S. Gaubert, B. Lemmens, R. Nussbaum.
  Iteration of order preserving subhomogeneous maps on a cone, in: Math. Proc. Cambridge Philos. Soc., 2006, vol. 140, n^o 1, pp. 157–176.
  http://www.arxiv.org/abs/math.DS/0410084
• 5M. Akian, A. Sulem, M. Taksar.
  Dynamic optimisation of long term growth rate for a portfolio with transaction costs and logarithmic utility, in: Mathematical Finance, 2001, vol. 11, n^o 2, pp. 153–188.
• 6F. Baccelli, G. Cohen, G. Olsder, J.-P. Quadrat.
  Synchronisation and Linearity, Wiley, 1992.
• 7J. Cochet-Terrasson, S. Gaubert, J. Gunawardena.
  A constructive fixed point theorem for min-max functions, in: Dynamics and Stability of Systems, 1999, vol. 14, n^o 4.
• 8G. Cohen, S. Gaubert, J.-P. Quadrat.
  Duality and Separation Theorems in Idempotent Semimodules, in: Linear Algebra and Appl., 2004, vol. 379, pp. 395–422.
  http://arxiv.org/abs/math.FA/0212294
• 9G. Cohen, S. Gaubert, J.-P. Quadrat.
  Max-plus algebra and system theory: where we are and where to go now, in: Annual Reviews in Control, 1999, vol. 23, pp. 207–219.
• 10S. Gaubert, J. Gunawardena.
  The Perron-Frobenius Theorem for Homogeneous, Monotone Functions, in: Trans. of AMS, 2004, vol. 356, n^o 12, pp. 4931-4950.
  http://www.ams.org/tran/2004-356-12/S0002-9947-04-03470-1/home.html, http://arxiv.org/abs/math.FA/0105091

Publications of the year

Doctoral Dissertations and Habilitation Theses

• 11V. Magron.
  Preuves formelles pour l'optimisation globale – Méthodes de gabarits et sommes de carrés, Ecole Polytechnique X, December 2013.
  http://hal.inria.fr/pastel-00917779
• 12Z. Qu.
  Théorie de Perron-Frobenius non linéaire et méthodes numériques max-plus pour la résolution d'équations d'Hamilton-Jacobi, Ecole Polytechnique X, October 2013.
  http://hal.inria.fr/pastel-00927122

Articles in International Peer-Reviewed Journals

• 13A. Adjé, S. Gaubert, E. Goubault.
  Computing the smallest fixed point of order-preserving nonexpansive mappings arising in positive stochastic games and static analysis of programs, in: Journal of Mathematical Analysis and applications, February 2014, vol. 410, n^o 1, pp. 227-240, Preprint arXiv:0806.1160. [ DOI : 10.1016/j.jmaa.2013.07.076 ]
  http://hal.inria.fr/hal-00940804
• 14M. Akian, S. Gaubert, A. Marchesini.
  Tropical bounds for eigenvalues of matrices, in: Linear Algebra and its Applications, January 2014, 17 p, See also arXiv:1309.7319. [ DOI : 10.1016/j.laa.2013.12.021 ]
  http://hal.inria.fr/hal-00881205
• 15X. Allamigeon.
  On the Complexity of Strongly Connected Components in Directed Hypergraphs, in: Algorithmica, January 2013, Published on line. [ DOI : 10.1007/s00453-012-9729-0 ]
  http://hal.inria.fr/hal-00782846
• 16X. Allamigeon, S. Gaubert, E. Goubault.
  Computing the Vertices of Tropical Polyhedra using Directed Hypergraphs, in: Discrete and Computational Geometry, February 2013, vol. 49, n^o 2, pp. 247-279. [ DOI : 10.1007/s00454-012-9469-6 ]
  http://hal.inria.fr/hal-00782862
• 17X. Allamigeon, R. Katz.
  Minimal external representations of tropical polyhedra, in: Journal of Combinatorial Theory, Series A, 2013, vol. 120, n^o 4, pp. 907-940. [ DOI : 10.1016/j.jcta.2013.01.011 ]
  http://hal.inria.fr/hal-00782837
• 18O. Fercoq, M. Akian, M. Bouhtou, S. Gaubert.
  Ergodic Control and Polyhedral approaches to PageRank Optimization, in: IEEE Transactions on Automatic Control, 2013, vol. 58, n^o 1, pp. 134–148, See also arXiv:1011.2348. [ DOI : 10.1109/TAC.2012.2226103 ]
  http://hal.inria.fr/hal-00782749
• 19S. Friedland, S. Gaubert.
  Submodular spectral functions of principal submatrices of a hermitian matrix, extensions and applications, in: Linear Algebra and its Applications, May 2013, vol. 438, n^o 10, pp. 3872-3884. [ DOI : 10.1016/j.laa.2011.11.021 ]
  http://hal.inria.fr/hal-00940794
• 20S. Friedland, S. Gaubert, L. Han.
  Perron–Frobenius theorem for nonnegative multilinear forms and extensions, in: Linear Algebra Appl., 2013, vol. 438, n^o 2, pp. 738–749. [ DOI : 10.1016/j.laa.2011.02.042 ]
  http://hal.inria.fr/hal-00782755
• 21S. Gaubert, Z. Qu.
  The contraction rate in Thompson metric of order-preserving flows on a cone - application to generalized Riccati equations, in: Journal of Differential Equations, February 2014, vol. published on line. [ DOI : 10.1016/j.jde.2014.01.024 ]
  http://hal.inria.fr/hal-00783972
• 22S. Gaubert, S. Sergeev.
  The level set method for the two-sided eigenproblem, in: Discrete Event Dynamic Systems, June 2013, vol. 23, n^o 2, pp. 105-134. [ DOI : 10.1007/s10626-012-0137-z ]
  http://hal.inria.fr/hal-00940791
• 23P. Poncet.
  How regular can maxitive measures be?, in: Topology and its Applications, March 2013, vol. 160, n^o 4, pp. 606-619. [ DOI : 10.1016/j.topol.2013.01.007 ]
  http://hal.inria.fr/hal-00922372

International Conferences with Proceedings

• 24M. Akian, J. Cochet-Terrasson, S. Detournay, S. Gaubert.
  Solving multichain stochastic games with mean payoff by policy iteration, in: 52nd IEEE Conference on Decision and Control, Florence, Italy, IEEE, December 2013.
  http://hal.inria.fr/hal-00933689
• 25X. Allamigeon, S. Gaubert, V. Magron, B. Werner.
  Certification of Bounds of Non-linear Functions: the Templates Method, in: Conferences on Intelligent Computer Mathematics (CICM 2013), Bath, United Kingdom, J. Carette, D. Aspinall, C. Lange, P. Sojka, W. Windsteige (editors), Lecture Notes in Computer Science, Springer Berlin Heidelberg, July 2013, vol. 7961, pp. 51-65. [ DOI : 10.1007/978-3-642-39320-4_4 ]
  http://hal.inria.fr/hal-00932333
• 26X. Allamigeon, S. Gaubert, V. Magron, B. Werner.
  Certification of inequalities involving transcendental functions: combining SDP and max-plus approximation, in: European Control Conference (ECC'13), Zurich, Switzerland, 2013, pp. 2244 - 2250.
  http://hal.inria.fr/hal-00932348
• 27S. Gaubert, Z. Qu.
  Markov Operators on Cones and Non-Commutative Consensus, in: European control conference 2013, Zurich, Switzerland, July 2013.
  http://hal.inria.fr/hal-00935312
• 28Z. Qu.
  Contraction of Riccati Flows Applied to the Convergence Analysis of the Max-Plus Curse of Dimensionality Free Method, in: European control conference 2013, Zurich, Switzerland, July 2013.
  http://hal.inria.fr/hal-00935313

Conferences without Proceedings

• 29M. Akian, S. Gaubert.
  Policy iteration algorithm for zero-sum two player stochastic games: complexity bounds involving nonlinear spectral radii, in: ILAS, Providence, United States, June 2013.
  http://hal.inria.fr/hal-00933261
• 30M. Akian, S. Gaubert, A. Marchesini.
  Tropical bounds for eigenvalues, in: ILAS - 18th Conference of the International Linear Algebra Society, Providence, United States, June 2013.
  http://hal.inria.fr/hal-00932813
• 31X. Allamigeon.
  Tropicalizing the simplex algorithm, in: SIAM Conference on Control and its Applications (SIAM CT'13), San Diego, United States, July 2013.
  http://hal.inria.fr/hal-00932350
• 32X. Allamigeon, P. Benchimol, S. Gaubert, M. Joswig.
  Tropicalizing the simplex algorithm, in: ILAS 2013 - 18th Conference of the International Linear Algebra Society, Providence, RI, United States, June 2013.
  http://hal.inria.fr/hal-00930959
• 33X. Allamigeon, P. Benchimol, S. Gaubert, M. Joswig.
  Tropicalizing the Simplex Algorithm, in: SMAI 2013 - 6ème biennale des mathématiques appliquées et industrielles, Seignosse, France, May 2013, Poster présentant l'article arXiv:1308.0454.
  http://hal.inria.fr/hal-00930941
• 34S. Gaubert, Z. Qu.
  Dobrushin ergodicity coefficient for Markov operators on cones, and beyond, in: International Linear Algebra Society, Providence, United States, June 2013.
  http://hal.inria.fr/hal-00935284
• 35S. Gaubert, Z. Qu.
  Taux de contraction de flots croissants sur un cône et application au contrôle stochastique, in: SMAI, Seignosse, France, May 2013, preprint Arxiv: 1206.0448.
  http://hal.inria.fr/hal-00935291
• 36Z. Qu.
  Contraction of Riccati flows applied to the convergence analysis of a max-plus curse of dimensionality free method, in: SIAM conference on control and its applications, San diego, United States, July 2013, Presentation of the article Arxiv:1301:4777.
  http://hal.inria.fr/hal-00935300

Scientific Books (or Scientific Book chapters)

• 37M. Akian, S. Gaubert, A. Guterman.
  Tropical Cramer Determinants Revisited, in: International Workshop on Tropical/Idempotent Mathematics and Applications, G. Litvinov, S. Sergeev (editors), Contemporary Mathematics, AMS, 2013, 41 p, To appear, see also arXiv:1309.6298.
  http://hal.inria.fr/hal-00881203
• 38N. Beeker, S. Gaubert, C. Glusa, L. Liberti.
  Is the Distance Geometry Problem in NP?, in: Distance Geometry: Theory, Methods, and Applications, A. Mucherino, C. Lavor, L. Liberti, N. Maculan (editors), Springer, 2013, pp. 85-93. [ DOI : 10.1007/978-1-4614-5128-0_5 ]
  http://hal.inria.fr/hal-00782869
• 39F. Billy, J. Clairambault, O. Fercoq.
  Optimisation of cancer drug treatments using cell population dynamics, in: Mathematical Methods and Models in Biomedicine, U. Ledzewicz, H. Schättler, A. Friedman, E. Kashdan (editors), Lecture Notes on Mathematical Modelling in the Life Sciences, Springer New York, January 2013, 265 p. [ DOI : 10.1007/978-1-4614-4178-6_10 ]
  http://hal.inria.fr/hal-00770366

Other Publications

• 40M. Akian, S. Gaubert.
  Policy iteration for perfect information stochastic mean payoff games with bounded first return times is strongly polynomial, 2013, 17 p, Preprint arXiv:1310.4953.
  http://hal.inria.fr/hal-00881207
• 41M. Akian, S. Gaubert, M. Sharify.
  Log-majorization of the moduli of the eigenvalues of a matrix polynomial by tropical roots, 2013, 29 p, Preprint arXiv:1304.2967.
  http://hal.inria.fr/hal-00881196
• 42X. Allamigeon, P. Benchimol, S. Gaubert, M. Joswig.
  Combinatorial simplex algorithms can solve mean payoff games, 2013, 15 p.
  http://hal.inria.fr/hal-00930915
• 43X. Allamigeon, P. Benchimol, S. Gaubert, M. Joswig.
  Tropicalizing the simplex algorithm, 2013, 35 p.
  http://hal.inria.fr/hal-00930913
• 44X. Allamigeon, U. Fahrenberg, S. Gaubert, R. D. Katz, A. Legay.
  Tropical Fourier-Motzkin elimination, with an application to real-time verification, 2013, Preprint arXiv:1308.2122.
  http://hal.inria.fr/hal-00935072
• 45J. Bolte, S. Gaubert, G. Vigeral.
  Definable zero-sum stochastic games, 2013, 29 p.
  http://hal.inria.fr/hal-00777707
• 46S. Gaubert, T. Lepoutre.
  Discrete limit and monotonicity properties of the Floquet eigenvalue in an age structured cell division cycle model, 2013, 30 p.
  http://hal.inria.fr/hal-00773211
• 47S. Gaubert, Z. Qu.
  Dobrushin ergodicity coefficient for Markov operators on cones, and beyond, 2013, Arxiv: 1302:5226.
  http://hal.inria.fr/hal-00935272
• 48P. Poncet.
  Convexities on ordered structures have their Krein–Milman theorem, 2013, 34 p, Accepted for publication in Journal of Convex Analysis.
  http://hal.inria.fr/hal-00922374
• 49P. Poncet.
  The idempotent Radon–Nikodym theorem has a converse statement, 2013, 13 p, Accepted for publication in Information Sciences.
  http://hal.inria.fr/hal-00922377
• 50Z. Qu.
  Contraction of Riccati flows applied to the convergence analysis of a max-plus curse of dimensionality free method, 2013.
  http://hal.inria.fr/hal-00935270
• 51C. Walsh.
  Gauge-reversing maps on cones, and Hilbert and Thompson isometries, 2013, 36 p.
  http://hal.inria.fr/hal-00930929

References in notes

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  Stochastic games and applications, NATO Science Series C: Mathematical and Physical Sciences, Kluwer Academic Publishers, Dordrecht, 2003, vol. 570, x+473 p.
• 53M. Akian, R. Bapat, S. Gaubert.
  Perturbation of eigenvalues of matrix pencils and optimal assignment problem, in: C. R. Acad. Sci. Paris, Série I, 2004, vol. 339, pp. 103–108.
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• 54M. Akian, R. Bapat, S. Gaubert.
  Min-plus methods in eigenvalue perturbation theory and generalised Lidskii-Vishik-Ljusternik theorem, 2005.
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• 55M. Akian, R. Bapat, S. Gaubert.
  Asymptotics of the Perron Eigenvalue and Eigenvector using Max Algebra, in: C. R. Acad. Sci. Paris., 1998, vol. 327, Série I, pp. 927–932.
  http://hal.inria.fr/inria-00073240
• 56M. Akian, J. Cochet-Terrasson, S. Detournay, S. Gaubert.
  Policy iteration algorithm for zero-sum multichain stochastic games with mean payoff and perfect information, 2012, Submitted.
  http://fr.arxiv.org/abs/1208.0446, http://hal.inria.fr/hal-00773080
• 57M. Akian, S. Gaubert, A. Guterman.
  Tropical polyhedra are equivalent to mean payoff games, in: Internat. J. Algebra Comput., 2012, vol. 22, n^o 1, 1250001, 43 p. [ DOI : 10.1142/S0218196711006674 ]
  http://arxiv.org/abs/0912.2462
• 58M. Akian, S. Gaubert, V. Kolokoltsov.
  Set coverings and invertibility of functional Galois connections, in: Idempotent Mathematics and Mathematical Physics, G. Litvinov, V. Maslov (editors), Contemporary Mathematics, American Mathematical Society, 2005, pp. 19-51.
  http://arxiv.org/abs/math.FA/0403441
• 59M. Akian, S. Gaubert, V. 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.
  http://arxiv.org/abs/math.PR/0509279, http://hal.inria.fr/inria-00000218/en/
• 60M. Akian, S. Gaubert, A. Lakhoua.
  The max-plus finite element method for solving deterministic optimal control problems: basic properties and convergence analysis, in: SIAM J. Control Optim., 2008, vol. 47, n^o 2, pp. 817–848. [ DOI : 10.1137/060655286 ]
  http://www.arxiv.org/abs/math.OC/0603619
• 61M. Akian, S. Gaubert, C. Walsh.
  The max-plus Martin boundary, in: Doc. Math., 2009, vol. 14, pp. 195–240.
  http://arxiv.org/abs/math/0412408
• 62M. Akian, J.-P. Quadrat, M. Viot.
  Duality between probability and optimization, in: Idempotency, J. Gunawardena (editor), Publications of the Isaac Newton Institute, Cambridge University Press, 1998.
• 63X. Allamigeon, S. Gaubert, E. Goubault.
  Inferring Min and Max Invariants Using Max-plus Polyhedra, in: Proceedings of the 15th International Static Analysis Symposium (SAS'08), Springer, 2008, vol. 5079, Valencia, Spain, 16-18 July 2008.
• 64X. Allamigeon, S. Gaubert, E. Goubault.
  The tropical double description method, in: Proceedings of the 27th International Symposium on Theoretical Aspects of Computer Science (STACS'2010), Nancy, France, March 4-6 2010.
  http://drops.dagstuhl.de/opus/volltexte/2010/2443/pdf/1001.AllamigeonXavier.2443.pdf
• 65N. Bacaër.
  Perturbations singulières et théorie spectrale min-plus, Université Paris 6, January 2002.
• 66F. Baccelli, D. Hong.
  TCP is max-plus linear and what it tells us on its throughput, in: Proceedings of the conference on Applications, Technologies, Architectures, and Protocols for Computer Communication, 2000, pp. 219-230.
• 67R. Bapat.
  A max version of the Perron-Frobenius theorem, in: Linear Algebra Appl., 1998, vol. 275/276, pp. 3–18.
• 68R. Bapat, T. Raghavan.
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• 69R. J. Bayardo, B. Panda.
  Fast Algorithms for Finding Extremal Sets, in: Proceedings of the SIAM International Conference on Data Mining, SDM 2011, SIAM, 2011.
• 70A. Benveniste, S. Gaubert, C. Jard.
  Monotone rational series and max-plus algebraic models of real-time systems, in: Proc. of the Fourth Workshop on Discrete Event Systems (WODES98), Cagliari, Italy, IEE, 1998.
• 71A. Berenstein, A. N. Kirillov.
  The Robinson-Schensted-Knuth bijection, quantum matrices, and piece-wise linear combinatorics, in: Proceedings of FPSAC'01, 2001.
• 72F. Billy, J. Clairambault, O. Fercoq, S. Gaubert, T. Lepoutre, T. Ouillon.
  Proliferation in Cell Population Models with Age Structure, in: AIP Conf. Proc., 2011, vol. 1389, pp. 1212-1215.
  http://dx.doi.org/10.1063/1.3637834
• 73F. Billy, J. Clairambault, O. Fercoq, S. Gaubert, T. Lepoutre, T. Ouillon, S. Saito.
  Synchronization and control of proliferation in cycling cell population models with age structure, in: Mathematics and Computers in Simulation, 2012, Published on line.
  http://dx.doi.org/10.1016/j.matcom.2012.03.005, http://hal.archives-ouvertes.fr/hal-00662885
• 74T. Blyth, M. Janowitz.
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• 75F. Bonnans, S. Gaubert.
  Recherche opérationnelle: aspects mathématiques et applications, École Polytechnique, 2012, Huitième édition, 180 pages.
• 76H. Braker.
  Algorithms and Applications in Timed Discrete Event Systems, Delft University of Technology, Dec 1993.
• 77S. Burns.
  Performance analysis and optimization of asynchronous circuits, Caltech, 1990.
• 78P. Butkovič.
  Max-algebra: the linear algebra of combinatorics?, in: Linear Algebra and Appl., 2003, vol. 367, pp. 313-335.
• 79Z. Cao, K. Kim, F. Roush.
  Incline algebra and applications, Ellis Horwood, 1984.
• 80C.-S. Chang.
  Performance guarantees in Communication networks, Springer, 2000.
• 81W. Chou, R. Griffiths.
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• 82P. Chretienne.
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• 83J. Cochet-Terrasson.
  Algorithmes d'itération sur les politiques pour les applications monotones contractantes, École des Mines, Dec. 2001.
• 84J. Cochet-Terrasson, S. Gaubert.
  A policy iteration algorithm for zero-sum stochastic games with mean payoff, in: C. R. Math. Acad. Sci. Paris, 2006, vol. 343, n^o 5, pp. 377–382.
• 85J. Cochet-Terrasson, G. Cohen, S. Gaubert, M. Mc Gettrick, J.-P. Quadrat.
  Numerical computation of spectral elements in max-plus algebra, in: Proc. of the IFAC Conference on System Structure and Control, Nantes, July 1998.
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• 88A. Costan, S. Gaubert, E. Goubault, M. Martel, S. Putot.
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• 98V. Dhingra, S. Gaubert.
  How to solve large scale deterministic games with mean payoff by policy iteration, in: Valuetools '06: Proceedings of the 1st international conference on Performance evaluation methodologies and tools, New York, NY, USA, ACM Press, 2006, 12 p.
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• 99M. Di Loreto, S. Gaubert, R. Katz, J.-J. Loiseau.
  Duality between invariant spaces for max-plus linear discrete event systems, in: SIAM J. Control Optim., 2010, vol. 48, n^o 8, pp. 5606-5628.
  http://arxiv.org/abs/0901.2915, http://hal.archives-ouvertes.fr/hal-00411243/en/
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  Derivation of the Fundamental Diagram for Two Circular Roads and a Crossing Using Minplus Algebra and Petri Net Modeling, in: Proceedings of the joint 44th IEEE Conference on Decision and Control and European Control Conference ECC 2005 (CDC-ECC'05), Seville, Espagne, 2005.
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