EN FR
EN FR


previous Previous | up Home


Bibliography

Major publications by the team in recent years
  • 1M. Akian, S. Gaubert, R. Bapat.

    Non-archimedean valuations of eigenvalues of matrix polynomials, in: Linear Algebra and its Applications, June 2016, vol. 498, pp. 592–627, Also arXiv:1601.00438. [ DOI : 10.1016/j.laa.2016.02.036 ]

    https://hal.inria.fr/hal-01251803
  • 2M. 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.

    http://dx.doi.org/10.1142/S0218196711006674
  • 3M. 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, Also arXiv:1201.1536. [ DOI : 10.1090/S0002-9947-2015-06413-7 ]

    https://hal.inria.fr/hal-00783682
  • 4M. Akian, S. Gaubert, C. Walsh.

    The max-plus Martin boundary, in: Doc. Math., 2009, vol. 14, pp. 195–240.
  • 5X. Allamigeon, P. Benchimol, S. Gaubert.

    The Tropical Shadow-Vertex Algorithm Solves Mean Payoff Games in Polynomial Time on Average, in: ICALP 2014, Lecture Notes in Computer Science, Springer, 2014, vol. 8572, pp. 89–100.

    http://dx.doi.org/10.1007/978-3-662-43948-7_8
  • 6X. Allamigeon, P. Benchimol, S. Gaubert, M. Joswig.

    Combinatorial simplex algorithms can solve mean payoff games, in: SIAM J. Opt., 2015, vol. 24, no 4, pp. 2096–2117.
  • 7X. Allamigeon, S. Gaubert, E. Goubault, S. Putot, N. Stott.

    A scalable algebraic method to infer quadratic invariants of switched systems, in: Proceedings of the International Conference on Embedded Software (EMSOFT), 2015.
  • 8J. Bolte, S. Gaubert, G. Vigeral.

    Definable zero-sum stochastic games, in: Mathematics of Operations Research, 2014, vol. 40, no 1, pp. 171–191, Also arXiv:1301.1967.

    http://dx.doi.org/10.1287/moor.2014.0666
  • 9S. Gaubert, T. Lepoutre.

    Discrete limit and monotonicity properties of the Floquet eigenvalue in an age structured cell division cycle model, in: J. Math. Biol., 2015.

    http://dx.doi.org/10.1007/s00285-015-0874-3
  • 10S. Gaubert, G. Vigeral.

    A maximin characterization of the escape rate of nonexpansive mappings in metrically convex spaces, in: Math. Proc. of Cambridge Phil. Soc., 2012, vol. 152, pp. 341–363, Also arXiv:1012.4765.

    http://dx.doi.org/10.1017/S0305004111000673
  • 11C. Walsh.

    The horofunction boundary and isometry group of the Hilbert geometry, in: Handbook of Hilbert Geometry, IRMA Lectures in Mathematics and Theoretical Physics, European Mathematical Society, 2014, vol. 22.

    https://hal.inria.fr/hal-00782827
Publications of the year

Doctoral Dissertations and Habilitation Theses

Articles in International Peer-Reviewed Journals

  • 13M. Akian, S. Gaubert, R. Bapat.

    Non-archimedean valuations of eigenvalues of matrix polynomials, in: Linear Algebra and its Applications, June 2016, vol. 498, pp. 592–627, Also arXiv:1601.00438. [ DOI : 10.1016/j.laa.2016.02.036 ]

    https://hal.inria.fr/hal-01251803
  • 14M. 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, Also arXiv:1201.1536. [ DOI : 10.1090/S0002-9947-2015-06413-7 ]

    https://hal.inria.fr/hal-00783682
  • 15M. Akian, S. Gaubert, M. Sharify.

    Log-majorization of the moduli of the eigenvalues of a matrix polynomial by tropical roots, in: Linear Algebra and its Applications, 2017, Also arXiv:1304.2967. [ DOI : 10.1016/j.laa.2016.11.004 ]

    https://hal.inria.fr/hal-00881196
  • 16X. Allamigeon, S. Gaubert, E. Goubault, S. Putot, N. Stott.

    A scalable algebraic method to infer quadratic invariants of switched systems, in: ACM Transactions on Embedded Computing Systems (TECS), August 2016, vol. 15, no 4. [ DOI : 10.1145/2932187 ]

    https://hal.inria.fr/hal-01423744
  • 17S. Gaubert, Z. Qu.

    Checking the strict positivity of Kraus maps is NP-hard, in: Information Processing Letters, February 2017, vol. 118, pp. 35–43, Also preprint arXiv:1402.1429. [ DOI : 10.1016/j.ipl.2016.09.008 ]

    https://hal.inria.fr/hal-01097942
  • 18S. Gaubert, Z. QU, S. Sridharan.

    Maximizing concave piecewise affine functions on the unitary group, in: Optimization Letters, April 2016, vol. 10, no 4, pp. 655-665. [ DOI : 10.1007/s11590-015-0951-y ]

    https://hal.inria.fr/hal-01248813
  • 19M. MacCaig.

    On scaling to an integer matrix and graphs with integer weighted cycles, in: Linear Algebra and Applications, June 2016, vol. 498, pp. 490–520. [ DOI : 10.1016/j.laa.2016.01.018 ]

    https://hal.inria.fr/hal-01423517
  • 20M. MacCaig.

    Exploring the complexity of the integer image problem in the max-algebra, in: Discrete Applied Mathematics, January 2017, vol. 217, no 2, pp. 261–275. [ DOI : 10.1016/j.dam.2016.09.016 ]

    https://hal.inria.fr/hal-01423520
  • 21A. Niv, L. Rowen.

    Dependence of tropical eigenspaces, in: Communications in Algebra, 2017, vol. 45, no 3, pp. 924-942. [ DOI : 10.1080/00927872.2016.1172603 ]

    https://hal.inria.fr/hal-01253422

Invited Conferences

  • 22M. Akian.

    Majorization inequalities for valuations of eigenvalues using tropical algebra, in: Emerging Trends in Applied Mathematics and Mechanics (ETAMM), Perpignan, France, May 2016.

    https://hal.inria.fr/hal-01425463
  • 23M. Akian.

    Solving Hamilton-Jacobi-Bellman equations by combining a max-plus linear approximation and a probabilistic numerical method, in: Workshop “Numerical methods for Hamilton-Jacobi equations in optimal control and related fields” at the Radon Institute, Austrian Academy of Sciences, Linz, Austria, November 2016.

    https://hal.inria.fr/hal-01425485
  • 24S. Gaubert.

    Zero-sum games, non-archimedean convexity and sinuous central paths, in: Workshop: Advances in Convex Analysis and Optimization, Erice, Italy, July 2016.

    https://hal.inria.fr/hal-01428994
  • 25S. Gaubert.

    Zero-sum games, non-archimedean convexity and sinuous central paths, in: 2016 Conference on Applied Mathematics, Hong Kong, China, August 2016.

    https://hal.inria.fr/hal-01428997

International Conferences with Proceedings

  • 26M. Akian, E. Fodjo.

    A probabilistic max-plus numerical method for solving stochastic control problems, in: 55th Conference on Decision and Control (CDC 2016), Las Vegas, United States, December 2016, Also arXiv:1605.02816.

    https://hal.inria.fr/hal-01425344
  • 27M. Akian, 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, United States, July 2016.

    https://hal.inria.fr/hal-01425473
  • 28X. Allamigeon, V. Boeuf, S. Gaubert.

    Stationary solutions of discrete and continuous Petri nets with priorities, in: 10th EAI International Conference on Performance Evaluation Methodologies and Tools, Taormina, France, 10th EAI International Conference on Performance Evaluation Methodologies and Tools, October 2016, 13 pages, 3 figures + 1 table. The version appearing in the proceedings of the conference VALUETOOLS 2016 is an extended abstract.

    https://hal.inria.fr/hal-01421885
  • 29X. Allamigeon, S. Gaubert, M. Skomra.

    Solving Generic Nonarchimedean Semidefinite Programs Using Stochastic Game Algorithms, in: ISSAC '16: International Symposium on Symbolic and Algebraic Computation, Waterloo, France, Proceedings of the ACM on International Symposium on Symbolic and Algebraic Computation (ISSAC'16), ACM, July 2016, Also arXiv:1603.06916. [ DOI : 10.1145/2930889.2930935 ]

    https://hal.inria.fr/hal-01422638
  • 30A. Hochart.

    An Accretive Operator Approach to Ergodic Problems for Zero-Sum Games, in: 22nd International Symposium on Mathematical Theory of Networks and Systems (MTNS), Minneapolis, United States, July 2016.

    https://hal.inria.fr/hal-01425315

Conferences without Proceedings

  • 31M. Akian, M. Bouhtou, J. B. Eytard, S. Gaubert.

    Price incentives in mobile networks: a tropical approach, in: PGMO Days, Palaiseau, France, November 2016.

    https://hal.inria.fr/hal-01425352
  • 32X. Allamigeon.

    Long and winding central paths, in: Emerging Trends in Applied Mathematics and Mechanics (ETAMM), Perpignan, France, May 2016.

    https://hal.inria.fr/hal-01428770
  • 33X. Allamigeon, S. Gaubert, M. Skomra.

    Solving Generic Nonarchimedean Semidefinite Programs using Stochastic Game Algorithms, in: PGMO Days, Palaiseau, France, November 2016.

    https://hal.inria.fr/hal-01429021
  • 34V. Boeuf.

    Évaluation de performance en réception d'appels d'urgence : débits asymptotiques dans un réseau de Pétri avec priorités, in: Congrès annuel de la société Française de Recherche Opérationnelle et d’Aide à la Décision (ROADEF), Compiègne, France, February 2016.

    https://hal.inria.fr/hal-01428975
  • 35E. Fodjo.

    A probabilistic max-plus numerical method for solving stochastic control problems, in: SIAM Conference on Financial Mathematics & Engineering, Austin, United States, November 2016.

    https://hal.inria.fr/hal-01425335
  • 36S. Gaubert.

    Ergodicity conditions in non-linear Perron-Frobenius theory and application to nonnegative tensors, in: International Conference on Tensors, Matrices and their Applications, Tianjin, China, May 2016.

    https://hal.inria.fr/hal-01428984
  • 37S. Gaubert.

    Stochastic mean payoff games are tropical semidefinite programs, in: SIAM Conference on Discrete Mathematics, Atlanta, United States, June 2016.

    https://hal.inria.fr/hal-01428990
  • 38A. Hochart.

    Une approche opérateur accrétif pour les jeux stochastiques avec critère ergodique, in: Conference SMAI-MODE, Toulouse, France, March 2016.

    https://hal.inria.fr/hal-01429185
  • 39M. MacCaig.

    Scaling to integer matrices in max-algebra, in: 20th Conference of the International Linear Algebra Society (ILAS), Leuven, Belgium, July 2016, Tropical symposium.

    https://hal.inria.fr/hal-01428924
  • 40A. Niv.

    Introduction to tropical total positivity, in: Recent advances in linear algebra and graph-theory, Chattanooga, United States, March 2016.

    https://hal.inria.fr/hal-01425299
  • 41A. Niv.

    Total non-negativity via valuations in tropical algebra, in: 20th Conference of the International Linear Algebra Society (ILAS), Leuven, Belgium, July 2016, Tropical symposium.

    https://hal.inria.fr/hal-01425308
  • 42M. Skomra.

    Les spectrahèdres tropicaux et leur relation aux jeux stochastiques, in: Conference SMAI-MODE, Toulouse, France, March 2016.

    https://hal.inria.fr/hal-01429006
  • 43M. Skomra.

    Nonarchimedean semidefinite programming and stochastic games, in: 20th Conference of the International Linear Algebra Society (ILAS), Leuven, Belgium, July 2016, Tropical symposium.

    https://hal.inria.fr/hal-01428932
  • 44M. Skomra.

    Nonarchimedean semidefinite programming and stochastic games, in: Emerging Trends in Applied Mathematics and Mechanics (ETAMM), Perpignan, France, May 2016.

    https://hal.inria.fr/hal-01428789
  • 45C. Walsh.

    Studying isometry groups using the horofunction boundary, in: New Methods in Finsler Geometry, Leipzig, Germany, July 2016.

    https://hal.inria.fr/hal-01428906

Scientific Books (or Scientific Book chapters)

Other Publications

References in notes
  • 54M. Akian, S. Gaubert.

    Spectral theorem for convex monotone homogeneous maps, and ergodic control, in: Nonlinear Anal., 2003, vol. 52, no 2, pp. 637–679.

    http://dx.doi.org/10.1016/S0362-546X(02)00170-0
  • 55M. 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
  • 56M. 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
  • 57M. 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
  • 58M. 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
  • 59M. 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
  • 60M. 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, Proceedings of the 54th IEEE Annual Conference on Decision and Control (CDC), Osaka, 2015, December 2015.

    https://hal.inria.fr/hal-01249321
  • 61X. 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
  • 62X. 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, Formal Modeling and Analysis of Timed Systems, Springer, September 2015, vol. 9268. [ DOI : 10.1007/978-3-319-22975-1_2 ]

    https://hal.inria.fr/hal-01248814
  • 63X. Allamigeon, S. Gaubert, É. Goubault.

    Inferring Min and Max Invariants Using Max-plus Polyhedra, in: Proceedings of the 15th International Static Analysis Symposium (SAS'08), Valencia, Spain, LNCS, Springer, 2008, vol. 5079, pp. 189–204.

    http://dx.doi.org/10.1007/978-3-540-69166-2_13
  • 64X. Allamigeon, S. Gaubert, E. Goubault.

    Computing the Vertices of Tropical Polyhedra using Directed Hypergraphs, in: Discrete Comp. Geom., 2012, Published on line. [ DOI : 10.1007/s00454-012-9469-6 ]

    http://fr.arxiv.org/abs/0904.3436v3
  • 65X. Allamigeon, S. Gaubert, E. Goubault, S. Putot, N. Stott.

    A scalable algebraic method to infer quadratic invariants of switched systems, in: International Conference on Embedded Software (EMSOFT'2015), Amsterdam, Netherlands, International Conference on Embedded Software (EMSOFT'2015), Alain Girault, Inria, Grenoble, France and Nan Guan, Northeastern University, China, October 2015. [ DOI : 10.1109/EMSOFT.2015.7318262 ]

    https://hal.inria.fr/hal-01249320
  • 66F. Baccelli, G. Cohen, G.-J. Olsder, J.-P. Quadrat.

    Synchronization and linearity: an algebra for discrete event systems, Wiley, 1992.
  • 67G. Barles, S. Mirrahimi, B. Perthame.

    Concentration in Lotka-Volterra parabolic or integral equations: a general convergence result, in: Methods Appl. Anal., 2009, vol. 16, no 3, pp. 321–340.

    http://dx.doi.org/10.4310/MAA.2009.v16.n3.a4
  • 68P. Butkovič.

    Max-algebra: the linear algebra of combinatorics?, in: Linear Algebra and its applications, 2003, vol. 367, pp. 313–335.
  • 69P. Butkovič.

    Max-linear systems: theory and algorithms, Springer Monographs in Mathematics, Springer-Verlag London, Ltd., London, 2010, xviii+272 p.

    http://dx.doi.org/10.1007/978-1-84996-299-5
  • 70J. 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.
  • 71G. 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.
  • 72A. Connes, C. Consani.

    Geometry of the arithmetic site, 2015, arXiv:1502.05580.
  • 73P. 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.
  • 74J. 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.
  • 75J.-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.
  • 76A. Deza, T. Terlaky, Y. Zinchenko.

    Polytopes and arrangements: diameter and curvature, in: Operations Research Letters, 2008, vol. 36, no 2, pp. 215–222.
  • 77A. 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
  • 78A. 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
  • 79A. Fathi, A. Siconolfi.

    Existence of C1 critical subsolutions of the Hamilton-Jacobi equation, in: Invent. Math., 2004, vol. 155, no 2, pp. 363–388.

    http://dx.doi.org/10.1007/s00222-003-0323-6
  • 80O. Fercoq, M. Akian, M. Bouhtou, S. Gaubert.

    Ergodic control and polyhedral approaches to PageRank optimization, in: IEEE Trans. Automat. Control, 2013, vol. 58, no 1, pp. 134–148.

    http://dx.doi.org/10.1109/TAC.2012.2226103
  • 81W. Fleming, W. McEneaney.

    A max-plus based algorithm for an HJB equation of non-linear filtering, in: SIAM J. Control and Opt., 2000, pp. 683–710.
  • 82S. 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
  • 83S. Gaubert, E. Goubault, A. Taly, S. Zennou.

    Static Analysis by Policy Iteration in Relational Domains, in: Proceedings of the Proc. of the 16th European Symposium on Programming (ESOP'07), Braga (Portugal), LNCS, Springer, 2007, vol. 4421, pp. 237–252.

    http://dx.doi.org/10.1007/978-3-540-71316-6_17
  • 84S. Gaubert, W. McEneaney, Z. Qu.

    Curse of dimensionality reduction in max-plus based approximation methods: theoretical estimates and improved pruning algorithms, in: Proceedings of the 50th IEEE Conference on Decision and Control and European Control Conference (CDC-ECC 11), Orlando, FL, USA, December 2011, pp. 1054-1061.

    http://arxiv.org/abs/1109.5241
  • 85S. Gaubert, M. Sharify.

    Tropical scaling of polynomial matrices, in: Positive systems, Berlin, Lecture Notes in Control and Inform. Sci., Springer, 2009, vol. 389, pp. 291–303.

    http://dx.doi.org/10.1007/978-3-642-02894-6_28
  • 86T. M. Gawlitza, H. Seidl, A. Adjé, S. Gaubert, E. Goubault.

    Abstract interpretation meets convex optimization, in: J. Symbolic Comput., 2012, vol. 47, no 12, pp. 1416–1446, Special issue on Invariant generation and reasoning about loops.

    http://dx.doi.org/10.1016/j.jsc.2011.12.048
  • 87I. M. Gelfand, M. M. Kapranov, A. V. Zelevinsky.

    Discriminants, resultants and multidimensional determinants, Modern Birkhäuser Classics, Birkhäuser Boston, Inc., Boston, MA, 2008, x+523 p, Reprint of the 1994 edition.
  • 88S. Hammarling, C. J. Munro, F. Tisseur.

    An algorithm for the complete solution of quadratic eigenvalue problems, in: ACM Trans. Math. Software, 2013, vol. 39, no 3, Art. 18, 19 p.

    http://dx.doi.org/10.1145/2450153.2450156
  • 89B. Heidergott, G. J. Olsder, J. van der Woude.

    Max Plus at Work: Modeling and Analysis of Synchronized Systems: A Course on Max-Plus Algebra and Its Applications, Princeton, 2005.
  • 90H. Ishii, H. Mitake.

    Representation formulas for solutions of Hamilton-Jacobi equations with convex Hamiltonians, in: Indiana Univ. Math. J., 2007, vol. 56, no 5, pp. 2159–2183.

    http://dx.doi.org/10.1512/iumj.2007.56.3048
  • 91I. Itenberg, G. Mikhalkin, E. Shustin.

    Tropical algebraic geometry, Oberwolfach Seminars, Birkhäuser Verlag, Basel, 2007, vol. 35, viii+103 p.
  • 92Z. Izhakian.

    Tropical arithmetic and matrix algebra, in: Comm. Algebra, 2009, vol. 37, no 4, pp. 1445–1468.

    http://dx.doi.org/10.1080/00927870802466967
  • 93H. Kaise, W. M. McEneaney.

    Idempotent expansions for continuous-time stochastic control: compact control space, in: Proceedings of the 49th IEEE Conference on Decision and Control, Atlanta, Dec. 2010.
  • 94V. Kolokoltsov, V. Maslov.

    Idempotent analysis and applications, Kluwer Acad. Publisher, 1997.
  • 95B. Lemmens, R. Nussbaum.

    Nonlinear Perron-Frobenius theory, Cambridge Tracts in Mathematics, Cambridge University Press, Cambridge, 2012, vol. 189, xii+323 p.

    http://dx.doi.org/10.1017/CBO9781139026079
  • 96Q. Lu, M. Madsen, M. Milata, S. Ravn, U. Fahrenberg, K. G. Larsen.

    Reachability Analysis for Timed Automata using Max-Plus Algebra, in: J. Logic Alg. Prog., 2012, vol. 81, no 3, pp. 298-313.
  • 97V. Maslov.

    Méthodes Operatorielles, Edition Mir, Moscou, 1987.
  • 98W. McEneaney, A. Deshpande, S. Gaubert.

    Curse-of-Complexity Attenuation in the Curse-of-Dimensionality-Free Method for HJB PDEs, in: Proc. of the 2008 American Control Conference, Seattle, Washington, USA, June 2008.
  • 99W. M. McEneaney, H. Kaise, S. H. Han.

    Idempotent Method for Continuous-time Stochastic Control and Complexity Attenuation, in: Proceedings of the 18th IFAC World Congress, 2011, Milano, Italie, 2011, pp. 3216-3221.
  • 100W. M. McEneaney.

    A curse-of-dimensionality-free numerical method for solution of certain HJB PDEs, in: SIAM J. Control Optim., 2007, vol. 46, no 4, pp. 1239–1276.

    http://dx.doi.org/10.1137/040610830
  • 101J.-F. Mertens, S. Sorin, S. Zamir.

    Repeated Games, Cambridge, 2015.
  • 102G. Mikhalkin.

    Enumerative tropical algebraic geometry in ℝ2, in: J. Amer. Math. Soc., 2005, vol. 18, no 2, pp. 313–377.

    http://dx.doi.org/10.1090/S0894-0347-05-00477-7
  • 103R. H. Möhring, M. Skutella, F. Stork.

    Scheduling with AND/OR precedence constraints, in: SIAM J. Comput., 2004, vol. 33, no 2, pp. 393–415.

    http://dx.doi.org/10.1137/S009753970037727X
  • 104A. 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
  • 105A. Papadopoulos.

    Metric spaces, convexity and non-positive curvature, IRMA Lectures in Mathematics and Theoretical Physics, Second, European Mathematical Society (EMS), Zürich, 2014, vol. 6, xii+309 p.

    http://dx.doi.org/10.4171/132
  • 106J.-E. Pin.

    Tropical Semirings, in: Idempotency, J. Gunawardena (editor), Publications of the Isaac Newton Institute, Cambridge University Press, 1998, vol. 11, pp. 50–69.
  • 107D. Reeb, M. J. Kastoryano, M. M. Wolf.

    Hilbert's projective metric in quantum information theory, in: J. Math. Phys., 2011, vol. 52, no 8, 082201, 33 p.

    http://dx.doi.org/10.1063/1.3615729
  • 108J. Richter-Gebert, B. Sturmfels, T. Theobald.

    First steps in tropical geometry, in: Idempotent mathematics and mathematical physics, Providence, RI, Contemp. Math., Amer. Math. Soc., 2005, vol. 377, pp. 289–317.
  • 109G. Sagnol, S. Gaubert, M. Bouhtou.

    Optimal monitoring on large networks by Successive c-Optimal Designs, in: Proceedings of the 22nd international teletraffic congress (ITC22), Amsterdam, The Netherlands, September, IEEE, 2010, [pdf]. [ DOI : 10.1109/ITC.2010.5608717 ]
  • 110S. Sankaranarayanan, H. Sipma, Z. Manna.

    Scalable Analysis of Linear Systems using Mathematical Programming, in: VMCAI, LNCS, 2005, vol. 3385.
  • 111R. Sepulchre, A. Sarlette, P. Rouchon.

    Consensus in noncommutative spaces, in: Proceedings of the 49th IEEE Conference on Decision and Control, Atlanta, USA, Dec 2010, pp. 6596-6601.

    http://dx.doi.org/10.1109/CDC.2010.5717072
  • 112I. Simon.

    Limited subsets of a free monoid, in: Proc. 19th Annual Symposium on Foundations of Computer Science, Piscataway, NJ, 1978, pp. 143–150.
  • 113H. L. Smith.

    Monotone dynamical systems, Mathematical Surveys and Monographs, American Mathematical Society, Providence, RI, 1995, vol. 41, x+174 p, An introduction to the theory of competitive and cooperative systems.
  • 114N. M. Tran, J. Yu.

    Product-Mix Auctions and Tropical Geometry, 2015.
  • 115O. Viro.

    Dequantization of real algebraic geometry on logarithmic paper, in: European Congress of Mathematics, Vol. I (Barcelona, 2000), Basel, Progr. Math., Birkhäuser, 2001, vol. 201, pp. 135–146.
  • 116O. Viro.

    Dequantization of real algebraic geometry on logarithmic paper, in: European Congress of Mathematics, Vol. I (Barcelona, 2000), Basel, Progr. Math., Birkhäuser, 2001, vol. 201, pp. 135–146.

    http://arxiv.org/abs/math.AG/0005163
  • 117C. Walsh.

    The horofunction boundary and isometry group of the Hilbert geometry, in: Handbook of Hilbert Geometry, A. Papadopoulos, M. Troyanov (editors), IRMA Lectures in Mathematics and Theoretical Physics, European Mathematical Society, 2014, vol. 22.

    https://hal.inria.fr/hal-00782827
  • 118C. Walsh.

    Hilbert and Thompson geometries isometric to infinite-dimensional Banach spaces, December 2015, working paper or preprint.

    https://hal.inria.fr/hal-01249343


previous Previous | up Home