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MAXPLUS - 2015
MAXPLUS - 2015
Team Maxplus
Members
Overall Objectives
Research Program
Application Domains
Highlights of the Year
New Software and Platforms
New Results
Bilateral Contracts and Grants with Industry
Partnerships and Cooperations
Dissemination
Bibliography
Team Maxplus
Members
Overall Objectives
Research Program
Application Domains
Highlights of the Year
New Software and Platforms
New Results
Bilateral Contracts and Grants with Industry
Partnerships and Cooperations
Dissemination
Bibliography


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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, no 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, no 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, no 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, no 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, no 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, no 12, pp. 4931-4950.

    http://www.ams.org/tran/2004-356-12/S0002-9947-04-03470-1/home.html
Publications of the year

Articles in International Peer-Reviewed Journals

  • 11M. Akian, S. Gaubert, A. Hochart.

    Ergodicity conditions for zero-sum games, in: Discrete and Continuous Dynamical Systems - Series A, September 2015, vol. 35, no 9, 31 p, See also arXiv: 1405.4658. [ DOI : 10.3934/dcds.2015.35.3901 ]

    https://hal.inria.fr/hal-01096206
  • 12M. Akian, S. Gaubert, R. Nussbaum.

    Uniqueness of the fixed point of nonexpansive semidifferentiable maps, in: Transactions of the American Mathematical Society, February 2016, vol. 368, no 2. [ DOI : 10.1090/S0002-9947-2015-06413-7 ]

    https://hal.inria.fr/hal-00783682
  • 13X. Allamigeon, P. Benchimol, S. Gaubert, M. Joswig.

    Tropicalizing the simplex algorithm, in: Siam Journal on Discrete Mathematics, April 2015, vol. 29, no 2, Preprint arXiv:1308.0454, 35 pages, 7 figures, 4 algorithms. Published in SIAM Journal on Discrete Mathematics. [ DOI : 10.1137/130936464 ]

    https://hal.inria.fr/hal-00930913
  • 14J. Bolte, S. Gaubert, G. Vigeral.

    Definable Zero-Sum Stochastic Games, in: Mathematics of Operations Research, 2015, vol. 40, no 1, pp. 171-191. [ DOI : 10.1287/moor.2014.0666 ]

    https://hal.archives-ouvertes.fr/hal-00777707
  • 15S. Gaubert, T. Lepoutre.

    Discrete limit and monotonicity properties of the Floquet eigenvalue in an age structured cell division cycle model, in: Journal of Mathematical Biology, December 2015, vol. 71, no 6, 30 pages. [ DOI : 10.1007/s00285-015-0874-3 ]

    https://hal.inria.fr/hal-00773211
  • 16S. Gaubert, Z. Qu.

    Dobrushin ergodicity coefficient for Markov operators on cones, in: Integral Equations and Operator Theory, January 2015, vol. 1, no 81, pp. 127-150, Also arXiv:1307.4649. [ DOI : 10.1007/s00020-014-2193-2 ]

    https://hal.inria.fr/hal-01099179
  • 17S. Gaubert, Z. Qu, S. Sridharan.

    Maximizing concave piecewise affine functions on the unitary group, in: Optimization Letters, September 2015. [ DOI : 10.1007/s11590-015-0951-y ]

    https://hal.inria.fr/hal-01248813
  • 18V. Magron, X. Allamigeon, S. Gaubert, B. Werner.

    Formal Proofs for Nonlinear Optimization, in: Journal of Formalized Reasoning, January 2015, vol. 8, no 15, pp. 1-24, Also ArXiv:1404.7282.

    https://hal.archives-ouvertes.fr/hal-00985675
  • 19A. Niv.

    On pseudo-inverses of matrices and their characteristic polynomials in supertropical algebra, in: Linear Algebra and its Applications, April 2015, vol. 471, pp. 264–290. [ DOI : 10.1016/j.laa.2014.12.038 ]

    https://hal.inria.fr/hal-01253421

Invited Conferences

  • 20M. Akian.

    Majorization inequalities for valuations of eigenvalues using tropical algebra, in: 4th International Conference on Matrix methods in Mathematics and Applications (MMMA-2015), Moscow, Russia, August 2015.

    https://hal.inria.fr/hal-01252363
  • 21M. Akian, S. Gaubert, A. Hochart.

    Ergodicity Condition for Zero-Sum Games, in: SIAM Conference on Control and its Applications (SIAM CT'15), Paris, France, July 2015.

    https://hal.inria.fr/hal-01252413
  • 22M. Akian, S. Gaubert, A. Marchesini, F. Tisseur.

    Hungarian Scaling of Polynomial Eigenproblems , in: SIAM Conference on Applied Linear Algebra (SIAM LA), Atlanta, United States, October 2015.

    https://hal.inria.fr/hal-01252398
  • 23X. Allamigeon, P. Benchimol, S. Gaubert.

    Tropicalizing Semialgebraic Pivoting Rules, Or How to Solve Mean Payoff Games in Polynomial Time on Average, in: SIAM Conference on Control and its Applications (SIAM CT’15), Paris, France, July 2015.

    https://hal.inria.fr/hal-01263357
  • 24X. Allamigeon, P. Benchimol, S. Gaubert, M. Joswig.

    Long and Winding Central Paths, in: SIAM Conference on Control and its Applications (SIAM CT’15), Paris, France, July 2015.

    https://hal.inria.fr/hal-01263337
  • 25A. Marchesini.

    Tropical diagonal scaling for asymptotic eigenvalue problems, in: The 8th International Congress on Industrial and Applied Mathematics (ICIAM), Beijing, China, August 2015.

    https://hal.inria.fr/hal-01253175

International Conferences with Proceedings

  • 26M. Akian, S. Gaubert, 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, Japan, December 2015.

    https://hal.inria.fr/hal-01249321
  • 27M. Akian, S. Gaubert, A. Marchesini.

    Tropical bounds for the eigenvalues of block structured matrices, in: SIAM Conference on Applied Linear Algebra (SIAM LA), Atlanta, United States, October 2015.

    https://hal.inria.fr/hal-01252379
  • 28X. Allamigeon, V. Boeuf, S. Gaubert.

    Performance evaluation of an emergency call center: tropical polynomial systems applied to timed Petri nets, in: 13th International Conference, Formal Modeling and Analysis of Timed Systems (FORMATS 2015), Madrid, Spain, Springer, September 2015, vol. 9268. [ DOI : 10.1007/978-3-319-22975-1_2 ]

    https://hal.inria.fr/hal-01248814
  • 30A. Hochart, M. Akian, S. Gaubert.

    Generic Uniqueness of the Bias Vector of Mean-Payoff Zero-Sum Games, in: SIAM Conference on Control and its Applications (SIAM CT’15), Paris, France, July 2015.

    https://hal.inria.fr/hal-01263363
  • 31N. Stott, X. Allamigeon, S. Gaubert, E. Goubault, S. Putot.

    Eigenvectors of Non-Linear Maps on the Cone of Positive Semidefinite Matrices Application to Stability Analysis, in: SIAM Conference on Control and its Applications (SIAM CT’15), Paris, France, July 2015.

    https://hal.inria.fr/hal-01263384
  • 32N. Stott, X. Allamigeon, S. Gaubert.

    Maximal Lower Bounds in the Loewner order, in: 2015 SIAM Conference on Applied Linear Algebra, Atlanta, United States, October 2015.

    https://hal.inria.fr/hal-01263476

Conferences without Proceedings

  • 33A. Niv.

    Factorization of tropical matrices, in: Tropical Algebraic Geometry Symposium 2015, Providence, Rhode Island, United States, Brown University, April 2015.

    https://hal.inria.fr/hal-01260232

Other Publications

References in notes
  • 39A. Neyman, S. Sorin (editors)

    Stochastic games and applications, NATO Science Series C: Mathematical and Physical Sciences, Kluwer Academic Publishers, Dordrecht, 2003, vol. 570, x+473 p.
  • 40M. 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.

    http://www.arxiv.org/abs/math.SP/0402438
  • 41M. Akian, R. Bapat, S. Gaubert.

    Min-plus methods in eigenvalue perturbation theory and generalised Lidskii-Vishik-Ljusternik theorem, 2005.

    http://arxiv.org/abs/math.SP/0402090
  • 42M. 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
  • 43M. Akian, S. Gaubert, A. Guterman.

    Linear independence over tropical semirings and beyond, in: Proceedings of the International Conference on Tropical and Idempotent Mathematics, G. Litvinov, S. Sergeev (editors), Contemporary Mathematics, American Mathematical Society, 2009, vol. 495, pp. 1-38.

    http://www.arxiv.org/abs/0812.3496
  • 44M. Akian, S. Gaubert, A. Guterman.

    Tropical polyhedra are equivalent to mean payoff games, in: Internat. J. Algebra Comput., 2012, vol. 22, no 1, 1250001, 43 p. [ DOI : 10.1142/S0218196711006674 ]

    http://arxiv.org/abs/0912.2462
  • 45M. Akian, S. Gaubert, A. Guterman.

    Tropical Cramer Determinants Revisited, in: Tropical and Idempotent Mathematics and Applications, G. Litvinov, S. Sergeev (editors), Contemporary Mathematics, AMS, 2014, vol. 616, 45 p, See also arXiv:1309.6298.

    https://hal.inria.fr/hal-00881203
  • 46M. 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
  • 47M. 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
  • 48M. 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, no 2, pp. 817–848. [ DOI : 10.1137/060655286 ]

    http://www.arxiv.org/abs/math.OC/0603619
  • 49M. Akian, S. Gaubert, A. Marchesini.

    Tropical bounds for eigenvalues of matrices, in: Linear Algebra and its Applications, April 2014, vol. 446, pp. 281–303, See also arXiv:1309.7319. [ DOI : 10.1016/j.laa.2013.12.021 ]

    https://hal.inria.fr/hal-00881205
  • 50M. Akian, S. Gaubert, M. Sharify.

    Log-majorization of the moduli of the eigenvalues of a matrix polynomial by tropical roots, 2013, Preprint arXiv:1304.2967, 29 pages, 5 figures.

    http://hal.inria.fr/hal-00881196
  • 51M. 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
  • 52M. 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.
  • 53X. Allamigeon, P. Benchimol, S. Gaubert.

    The tropical shadow-vertex algorithm solves mean payoff games in polynomial time on average, in: ICALP 2014, Copenhagen, France, J. Esparza, P. Fraigniaud, T. Husfeldt, E. Koutsoupias (editors), 41st International Colloquium, ICALP 2014, Copenhagen, Denmark, July 8-11, 2014, Proceedings, Part I, Springer, July 2014, vol. 8572, 12 p. [ DOI : 10.1007/978-3-662-43948-7_8 ]

    https://hal.inria.fr/hal-01096447
  • 54X. 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
  • 55X. 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
  • 56X. Allamigeon, P. Benchimol, S. Gaubert, M. Joswig.

    Combinatorial simplex algorithms can solve mean payoff games, in: SIAM Journal on Optimization, December 2014, vol. 24, no 4, 22 p, Preprint arXiv:1309.5925, 15 pages, 3 figures. [ DOI : 10.1137/140953800 ]

    https://hal.inria.fr/hal-00930915
  • 57X. Allamigeon, P. Benchimol, S. Gaubert, M. Joswig.

    Combinatorial Simplex Algorithms Can Solve Mean Payoff Games, in: The 21st International Symposium on Mathematical Theory of Networks and Systems (MTNS 2014), Groningen, Netherlands, July 2014.

    https://hal.inria.fr/hal-01097727
  • 58X. Allamigeon, P. Benchimol, S. Gaubert, M. Joswig.

    Combinatorial simplex algorithms can solve mean payoff games, in: 20th Conference of the International Federation of Operational Research Societies, Barcelone, Spain, July 2014.

    https://hal.inria.fr/hal-01097728
  • 59X. Allamigeon, P. Benchimol, S. Gaubert, M. Joswig.

    La méthode du simplexe tropical, in: ROADEF - 15ème congrès annuel de la Société française de recherche opérationnelle et d’aide à la décision, Bordeaux, France, Société française de recherche opérationnelle et d’aide à la décision (ROADEF), February 2014, arxiv 1308.0454.

    https://hal.inria.fr/hal-01097726
  • 60X. Allamigeon, P. Benchimol, S. Gaubert, M. Joswig.

    Long and winding central paths, May 2014, Preprint arXiv:1405.4161, v2 May 2015.

    https://hal.inria.fr/hal-01096452
  • 61X. 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.
  • 62X. 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
  • 63X. Allamigeon, S. Gaubert, E. Goubault.

    Computing the Vertices of Tropical Polyhedra using Directed Hypergraphs, in: Discrete and Computational Geometry, February 2013, vol. 49, no 2, pp. 247-279. [ DOI : 10.1007/s00454-012-9469-6 ]

    http://hal.inria.fr/hal-00782862
  • 64X. Allamigeon, R. Katz.

    Minimal external representations of tropical polyhedra, in: Journal of Combinatorial Theory, Series A, 2013, vol. 120, no 4, pp. 907-940. [ DOI : 10.1016/j.jcta.2013.01.011 ]

    http://hal.inria.fr/hal-00782837
  • 65X. Allamigeon, R. D. Katz.

    Tropicalization of facets of polytopes, August 2014, Preprint arXiv:1408.6176.

    https://hal.inria.fr/hal-01096435
  • 66N. Bacaër.

    Perturbations singulières et théorie spectrale min-plus, Université Paris 6, January 2002.
  • 67F. 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.
  • 68R. Bapat.

    A max version of the Perron-Frobenius theorem, in: Linear Algebra Appl., 1998, vol. 275/276, pp. 3–18.
  • 69R. Bapat, T. Raghavan.

    Nonnegative matrices and applications, Cambridge university press, 1997, no 64, XIII+336 p.
  • 70P. Benchimol.

    Tropical aspects of linear programming, Ecole Polytechnique, December 2014.

    https://hal-polytechnique.archives-ouvertes.fr/tel-01198482
  • 71A. 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.
  • 72A. Berenstein, A. N. Kirillov.

    The Robinson-Schensted-Knuth bijection, quantum matrices, and piece-wise linear combinatorics, in: Proceedings of FPSAC'01, 2001.
  • 73M. Bezem, R. Nieuwenhuis, E. Rodríguez-Carbonell.

    Exponential behaviour of the Butkovič-Zimmermann algorithm for solving two-sided linear systems in max-algebra, in: Discrete Appl. Math., 2008, vol. 156, no 18, pp. 3506–3509.

    http://dx.doi.org/10.1016/j.dam.2008.03.016
  • 74T. Blyth, M. Janowitz.

    Residuation Theory, Pergamon press, 1972.
  • 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.

    Ground states of one dimensional systems using effective potentials, in: Phys. Rev. B, 1986, vol. 34, pp. 6219–34.
  • 82P. Chretienne.

    Les Réseaux de Petri Temporisés, Thèse Université Pierre et Marie Curie (Paris VI), Paris, 1983.
  • 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, no 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.
  • 86G. Cohen, D. Dubois, J.-P. Quadrat, M. Viot.

    Analyse du comportement périodique des systèmes de production par la théorie des dioïdes, Inria, Le Chesnay, France, 1983, no 191.

    http://hal.inria.fr/inria-00076367
  • 87J.-P. Comet.

    Application of max-plus algebra to biological sequence comparison, in: Theor. Comput. Sci., Special issue on max-plus algebras, 2003, vol. 293, pp. 189–217.
  • 88A. Costan, S. Gaubert, E. Goubault, M. Martel, S. Putot.

    A policy iteration algorithm for computing fixed points in static analysis of programs, in: Proceedings of the 17th International Conference on Computer Aided Verification (CAV'05), Edinburgh, LNCS, Springer, July 2005, pp. 462–475.
  • 89P. Cousot, R. Cousot.

    Abstract Interpretation: A unified lattice model for static analysis of programs by construction of approximations of fixed points, in: Principles of Programming Languages 4, 1977, pp. 238–252.
  • 90P. Cousot, R. Cousot.

    Comparison of the Galois connection and widening/narrowing approaches to abstract interpretation. JTASPEFL'91, Bordeaux, in: BIGRE, October 1991, vol. 74, pp. 107–110.
  • 91M. Crandall, L. Tartar.

    Some relations between non expansive and order preserving maps, in: Proceedings of the AMS, 1980, vol. 78, no 3, pp. 385–390.
  • 92R. Cuninghame-Green.

    Minimax Algebra, Lecture notes in Economics and Mathematical Systems, Springer, 1979, no 166.
  • 93J. De Loera, B. Sturmfels, C. Vinzant.

    The central curve in linear programming, in: Foundations of Computational Mathematics, 2012, vol. 12, no 4, pp. 509–540.
  • 94J.-P. Dedieu, G. Malajovich, M. Shub.

    On the Curvature of the Central Path of Linear Programming Theory, in: Foundations of Computational Mathematics, 2005, vol. 5, no 2, pp. 145–171.
  • 95P. Del Moral.

    Maslov optimization theory: topological aspects, in: Idempotency (Bristol, 1994), Cambridge, Publ. Newton Inst., Cambridge Univ. Press, 1998, vol. 11, pp. 354–382.
  • 96P. Del Moral, T. Thuillet, G. Rigal, G. Salut.

    Optimal versus random processes : the nonlinear case, LAAS, 1990.
  • 97M. Develin, B. Sturmfels.

    Tropical convexity, in: Doc. Math., 2004, vol. 9, pp. 1–27.
  • 98M. Develin, J. Yu.

    Tropical polytopes and cellular resolutions, in: Experimental Mathematics, 2007, vol. 16, no 3, pp. 277–292.

    http://arxiv.org/abs/math/0605494
  • 99A. Deza, T. Terlaky, Y. Zinchenko.

    Polytopes and arrangements: diameter and curvature, in: Operations Research Letters, 2008, vol. 36, no 2, pp. 215–222.
  • 100A. Deza, T. Terlaky, Y. Zinchenko.

    Central path curvature and iteration-complexity for redundant Klee-Minty cubes, in: Advances in applied mathematics and global optimization, New York, Adv. Mech. Math., Springer, 2009, vol. 17, pp. 223–256.

    http://dx.doi.org/10.1007/978-0-387-75714-8_7
  • 101V. 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.

    http://doi.acm.org/10.1145/1190095.1190110
  • 102M. 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, no 8, pp. 5606-5628.

    http://arxiv.org/abs/0901.2915
  • 103M. Dubreil-Jacotin, L. Lesieur, R. Croisot.

    Leçons sur la Théorie des Treillis, des Structures Algébriques Ordonnées, et des Treillis géométriques, Cahiers Scientifiques, Gauthier Villars, Paris, 1953, vol. XXI.
  • 104A. Fahim, N. Touzi, X. Warin.

    A probabilistic numerical method for fully nonlinear parabolic PDEs, in: Ann. Appl. Probab., 2011, vol. 21, no 4, pp. 1322–1364.

    http://dx.doi.org/10.1214/10-AAP723
  • 105N. Farhi, M. Goursat, J.-P. Quadrat.

    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.
  • 106A. Fathi.

    Solutions KAM faibles et théorie de Mather sur les systèmes lagrangiens, in: C. R. Acad. Sci. Paris, Sér. I Math., 1997, vol. 324, no 9, pp. 1043–1046.
  • 107S. Fomin, A. Zelevinsky.

    Cluster algebras. I. Foundations, in: J. Amer. Math. Soc., 2002, vol. 15, no 2, pp. 497–529.

    http://arxiv.org/abs/math.RT/0104151
  • 108S. Friedland.

    Limit eigenvalues of nonnegative matrices, in: Linear Algebra and Its Applications, 1986, vol. 74, pp. 173–178.

    http://dx.doi.org/10.1016/0024-3795(86)90120-5
  • 109S. Gaubert.

    Performance Evaluation of (max,+) Automata, in: IEEE Trans. on Automatic Control, Dec 1995, vol. 40, no 12, pp. 2014–2025.
  • 110S. Gaubert, E. Goubault, A. Taly, S. Zennou.

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