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, p. 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, p. 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, p. 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, p. 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, p. 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, p. 207–219.
10S. Gaubert, J. Gunawardena.

The Perron-Frobenius Theorem for Homogeneous, Monotone Functions, in: Trans. of AMS, 2004, vol. 356, n^o 12, p. 4931-4950, Also arXiv:math.FA/0105091.

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

Publications of the year

Doctoral Dissertations and Habilitation Theses

11A. Adjé.

Optimisation et jeux appliqués à l'analyse statique par interprétation abstraite, École Polytechnique (France), Avril 2011.
12P. Poncet.

Infinite-dimensional idempotent analysis: the role of continuous posets, École Polytechnique (France), November 2011.
13M. Sharify.

Scaling Algorithms and Tropical Methods in Numerical Matrix Analysis, École Polytechnique (France), September 2011.

Articles in International Peer-Reviewed Journal

14A. Adjé, S. Gaubert, E. Goubault.

Coupling policy iteration with semi-definite relaxation to compute accurate numerical invariants in static analysis, in: Logical methods in computer science, 2011, To appear.

http://arxiv.org/abs/1111.5223
15M. Akian, S. Detournay.

Multigrid methods for two-player zero-sum stochastic games, in: Numerical Linear Algebra with Applications, 2011, To appear.

http://arxiv.org/abs/1107.1653
16M. Akian, S. Gaubert, A. Guterman.

Tropical polyhedra are equivalent to mean payoff games, in: International of Algebra and Computation, 2012, Published on line. [ DOI : 10.1142/S0218196711006674 ]

http://arxiv.org/abs/0912.2462
17M. Akian, S. Gaubert, B. Lemmens.

Stability and convergence in discrete convex monotone dynamical systems, in: Journal of Fixed Point Theory and Applications, 2011, vol. 9, n^o 2, p. 295-325. [ DOI : 10.1007/s11784-011-0052-1 ]

http://arxiv.org/abs/1003.5346
18M. Akian, S. Gaubert, V. Nitica, I. Singer.

Best approximation in max-plus semimodules, in: Linear Algebra and its Applications, 2011, vol. 435, n^o 12, p. 3261–3296. [ DOI : 10.1016/j.laa.2011.06.009 ]

http://arxiv.org/abs/1012.5492
19X. Allamigeon, S. Gaubert, R. Katz.

The number of extreme points of tropical polyhedra, in: J. Comb. Theory Series A, 2011, vol. 118, n^o 1, p. 162-189. [ DOI : 10.1016/j.jcta.2010.04.003 ]

http://arxiv.org/abs/0906.3492
20X. Allamigeon, S. Gaubert, R. Katz.

Tropical polar cones, hypergraph transversals, and mean payoff games, in: Linear Algebra and its Applications, 2011, vol. 435, n^o 7, p. 1549-1574. [ DOI : 10.1016/j.laa.2011.02.004 ]

http://arxiv.org/abs/1004.2778
21V. Blondel, S. Gaubert, N. Portier.

The set of realizations of a max-plus linear sequence is semi-polyhedral, in: Journal of Computer and System Sciences, July 2011, vol. 77, n^o 4, p. 820–833. [ DOI : 10.1016/j.jcss.2010.08.010 ]

http://arxiv.org/abs/1010.3685, http://hal.inria.fr/ensl-00507757/en
22J. Clairambault, S. Gaubert, T. Lepoutre.

Circadian rhythm and cell population growth, in: Mathematical and Computer Modelling, 2011, vol. 53, n^o 7-8, p. 1558–1567. [ DOI : 10.1016/j.mcm.2010.05.034 ]

http://arxiv.org/abs/1006.3459, http://hal.archives-ouvertes.fr/hal-00492983/fr/
23N. Farhi, M. Goursat, J.-P. Quadrat.

Piecewise linear concave dynamical systems appearing in the microscopic traffic modeling, in: Linear Algebra and Applications, 2011, vol. 435, n^o 7, p. 1711-1735.

http://dx.doi.org/10.1016/j.laa.2011.03.002
24S. Friedland, S. Gaubert.

Submodular spectral functions of principal submatrices of an hermitian matrix, in: Linear Algebra and Appl, 2011, Published on line, doi:10.1016/j.laa.2011.11.021.

http://arxiv.org/abs/1007.3478
25S. Friedland, S. Gaubert, L. Han.

Perron-Frobenius theorem for nonnegative multilinear forms and extensions, in: Linear Algebra and its Applications, 2011, Published on line. [ DOI : 10.1016/j.laa.2011.02.042 ]

http://arxiv.org/abs/0905.1626
26S. Gaubert, R. Katz.

Minimal half-spaces and external representation of tropical polyhedra, in: Journal of Algebraic Combinatorics, 2011, vol. 33, n^o 3, p. 325-348. [ DOI : 10.1007/s10801-010-0246-4 ]

http://arxiv.org/abs/0908.1586
27S. Gaubert, R. Katz, S. Sergeev.

Tropical linear-fractional programming and parametric mean payoff games, in: Journal of symbolic computation, 2011, To appear. Special issue on invariant generation and advanced techniques for reasoning about loops.

http://arxiv.org/abs/1101.3431
28S. Gaubert, W. McEneaney.

Min-max spaces and complexity reduction in min-max expansions, in: Appl. Math. Optim., 2011, To appear, doi:10.1007/s00245-011-9158-5.
29S. Gaubert, G. Vigeral.

A maximin characterization of the escape rate of nonexpansive mappings in metrically convex spaces, in: Math. Proc. of Cambridge Phil. Soc., 2011, Published on line. [ DOI : 10.1017/S0305004111000673 ]

http://arxiv.org/abs/1012.4765
30T. M. Gawlitza, H. Seidl, A. Adjé, S. Gaubert, E. Goubault.

Abstract Interpretation Meets Convex Optimization, in: J. Symbolic Computation, 2011, Special issue on Invariant generation and reasoning about loops, to appear.
31R. Katz, H. Schneider, S. Sergeev.

On commuting matrices in max algebra and in classical nonnegative algebra, in: Linear Algebra and Applications, 2012, vol. 436, n^o 2, p. 276-292.
32B. Lemmens, C. Walsh.

Isometries of polyhedral Hilbert geometries, in: J. Topol. Anal., 2011, vol. 3, n^o 2, p. 213–241.

http://dx.doi.org/10.1142/S1793525311000520
33V. Nitica, S. Sergeev.

An interval version of separation by semispaces in max-min convexity, in: Linear Algebra and Applications, 2011, vol. 435, n^o 7, p. 1637-1648.
34P. Poncet.

A decomposition theorem for maxitive measures, in: Linear Algebra and applications, 2011, vol. 435, n^o 7, p. 1672-1680. [ DOI : 10.1016/j.laa.2010.03.004 ]

http://arxiv.org/abs/0912.5178
35G. Sagnol.

A Class of Semidefinite Programs with rank-one solutions, in: Linear Algebra and its Applications, 2011, vol. 435, n^o 6, p. 1446-1463. [ DOI : 10.1016/j.laa.2011.03.027 ]

http://arxiv.org/pdf/0909.5577
36G. Sagnol.

Computing Optimal Designs of multiresponse Experiments reduces to Second-Order Cone Programming, in: Journal of Statistical Planning and Inference, 2011, vol. 141, n^o 5, p. 1684-1708. [ DOI : 10.1016/j.jspi.2010.11.031 ]

http://arxiv.org/abs/0912.5467
37S. Sergeev, H. Schneider.

CSR expansions of matrix powers in max algebra, in: Transactions of the American Mathematical Society, 2011, Accepted for publication.
38S. Sergeev.

Max-algebraic attraction cones of nonnegative irreducible matrices, in: Linear Algebra and Applications, 2011, vol. 435, n^o 7, p. 1736-1757.
39S. Sergeev.

On the problem $A x = λ B x$ in max algebra: every system of intervals is a spectrum, in: Kybernetika, 2011, vol. 47, n^o 5, p. 715-721.
40S. Sergeev, E. Wagneur.

Basic solutions of systems with two max-linear inequalities, in: Linear Algebra and Applications, 2011, vol. 435, n^o 7, p. 1758-1768.
41C. Walsh.

The action of a nilpotent group on its horofunction boundary has finite orbits, in: Groups Geom. Dyn., 2011, vol. 5, n^o 1, p. 189–206.

http://dx.doi.org/10.4171/GGD/122

International Conferences with Proceedings

42F. 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, p. 1212-1215.

http://dx.doi.org/10.1063/1.3637834
43S. 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, p. 1054-1061.

http://arxiv.org/abs/1109.5241

Conferences without Proceedings

44M. Akian, S. Detournay.

Multigrid methods for zero-sum stochastic games with mean reward, in: 15th Copper Mountain Conference on multigrids methods, Colorado, March 2011.
45M. Akian, S. Detournay.

Multigrid methods for zero-sum stochastic games with mean reward, in: 10th IMACS International Symposium on Iterative Methods in Scientific Computing, Marrakech, Morocco, May 18-21 2011.
46M. Akian, S. Gaubert, B. Lemmens.

Fixed points and convergence of discrete convex monotone dynamical systems, in: SIAM Conference on Control and Its Applications (CT11), Baltimore, USA, July 25-27 2011.
47X. Allamigeon.

Algorithmics of tropical polyhedra, and application to software verification, in: 17th Conference of the International Linear Algebra Society (ILAS), Braunschweig, Allemagne, Août 2011, (Joint work with S. Gaubert, E. Goubault, and R. Katz).
48O. Fercoq.

Perron vector Optimization applied to search engines, in: 10th IMACS International Symposium on Iterative Methods in Scientific Computing, Marrakech, Morocco, May 18-21 2011.
49S. Gaubert, G. Vigeral.

A Collatz-Wielandt theorem for nonexpansive mappings in metric spaces of nonpositive curvature, in: Conference on Matrix Methods in Mathematics and Applications, Moscow, June 2011.
50S. Sergeev.

Fiedler-Pták scaling in max algebra, in: 17th Conference of the International Linear Algebra Society (ILAS), Braunschweig, Allemagne, Août 2011.
51M. Sharify.

Scaling of matrix polynomials by means of tropical algebra, in: 17th Conference of the International Linear Algebra Society (ILAS), Braunschweig, Allemagne, Août 2011, (Joint work with S. Gaubert).

Scientific Books (or Scientific Book chapters)

52F. 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), Springer, 2011, To appear.

Internal Reports

53F. Bonnans, S. Gaubert.

Recherche opérationnelle: aspects mathématiques et applications, École Polytechnique, 2011, Septième édition, 180 p..

Other Publications

54M. Akian, J. Cochet-Terrasson, S. Detournay, S. Gaubert.

Policy iteration algorithm for zero-sum stochastic games with mean payoff, with application to the numerical solution of stationary Isaacs equations, 2011, Preprint.
55M. Akian, S. Gaubert, R. Nussbaum.

A Collatz-Wielandt characterization of the spectral radius of order-preserving homogeneous maps on cones, 2011.

http://arxiv.org/abs/1112.5968
56X. Allamigeon.

Strongly connected components of directed hypergraphs, 2011, Preprint. Submitted.

http://arxiv.org/abs/1112.1444
57X. Allamigeon, S. Gaubert, E. Goubault.

Computing the vertices of tropical polyhedra using directed hypergraphs, 2011, The 2011 version (v3, with important improvements) of this preprint initially posted in 2009 (v1) has been submitted..

http://arxiv.org/abs/0904.3436v3
58F. Billy, J. Clairambault, O. Fercoq, S. Gaubert, T. Lepoutre, T. Ouillon, S. Saito.

Control of proliferation in cycling cell population models with age structure, 2011, Submitted.
59P. Butkovič, H. Schneider, S. Sergeev.

Recognizing weakly stable systems, 2011, submitted.
60P. Butkovič, H. Schneider, S. Sergeev.

Z-matrix equations in max algebra, nonnegative linear algebra and other semirings, 2011, submitted.

http://arxiv.org/abs/1110.4564
61O. Fercoq, M. Akian, M. Bouhtou, S. Gaubert.

Ergodic Control and Polyhedral approaches to PageRank Optimization, 2011, Revised version (v2), accepted for publication in IEEE Transactions Autom. Control..

http://arxiv.org/abs/1011.2348
62O. Fercoq.

Perron vector optimization applied to search engines, 2011.

http://arxiv.org/abs/1111.2234
63M. Gavalec, I. Rashid, S. Sergeev.

Eigenspace of a three-dimensional max-Lukasiewicz fuzzy matrix, 2011, submitted.
64S. Mirrahimi, G. Raoul.

Dynamics of sexual populations structured by a space variable and a phenotypical trait, 2011, Submitted.
65S. Mirrahimi, P. Souganidis.

A homogeneization approach for the motion of motor proteins, 2011, Submitted.
66S. Sergeev.

An application of the max-plus spectral theory to an ultradiscrete analogue of the Lax pair, 2011, submitted.
67S. Sergeev.

Fiedler-Pták scaling in max algebra, 2011, submitted.
68S. Sergeev.

On the problem $A x = λ B x$ in max algebra: every system of intervals is a spectrum, Jan 2011, submitted.
69M. Sharify, S. Gaubert, L. Grigori.

A parallel preprocessing for the optimal assignment problem based on diagonal scaling, 2011, Submitted.

http://arxiv.org/abs/1104.3830
70C. Walsh.

The horoboundary and isometry group of Thurston's Lipschitz metric, 2011, Revised version 3, to appear in "Handbook of Teichmuller Theory", Volume 3.

http://www.arxiv.org/abs/1006.2158

References in notes

71A. 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.
72M. Akian.

Méthodes multigrilles en contrôle stochastique, Université Paris IX-Dauphine, Paris, 1990.
73M. 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, p. 103–108.

http://www.arxiv.org/abs/math.SP/0402438
74M. 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
75M. 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, p. 927–932.

http://hal.inria.fr/inria-00073240
76M. 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, p. 19-51.

http://arxiv.org/abs/math.FA/0403441
77M. 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, Also arXiv:math.PR/0509279.

http://hal.inria.fr/inria-00000218/en/
78M. 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, p. 817–848. [ DOI : 10.1137/060655286 ]

http://www.arxiv.org/abs/math.OC/0603619
79M. Akian, S. Gaubert, C. Walsh.

The max-plus Martin boundary, in: Doc. Math., 2009, vol. 14, p. 195–240.

http://arxiv.org/abs/math/0412408
80M. Akian, J. Menaldi, A. Sulem.

On an investment-consumption model with transaction costs, in: SIAM J. Control Optim., 1996, vol. 34, n^o 1, p. 329–364.
81M. 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.
82X. 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.
83X. 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
84N. Bacaër.

Perturbations singulières et théorie spectrale min-plus, Université Paris 6, January 2002.
85F. 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, p. 219-230.
86R. Bapat.

A max version of the Perron-Frobenius theorem, in: Linear Algebra Appl., 1998, vol. 275/276, p. 3–18.
87R. Bapat, T. Raghavan.

Nonnegative matrices and applications, Cambridge university press, 1997, n^o 64.
88R. J. Bayardo, B. Panda.

Fast Algorithms for Finding Extremal Sets, in: Proceedings of the SIAM International Conference on Data Mining, SDM 2011, SIAM, 2011, To appear..
89A. 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.
90A. Berenstein, A. N. Kirillov.

The Robinson-Schensted-Knuth bijection, quantum matrices, and piece-wise linear combinatorics, in: Proceedings of FPSAC'01, 2001.
91H. Bjorklund, S. Vorobyov.

A combinatorial strongly subexponential strategy improvement algorithm for mean payoff games, in: Discrete Appl. Math., 2007, vol. 155, p. 210-229.
92T. Blyth, M. Janowitz.

Residuation Theory, Pergamon press, 1972.
93H. Braker.

Algorithms and Applications in Timed Discrete Event Systems, Delft University of Technology, Dec 1993.
94S. Burns.

Performance analysis and optimization of asynchronous circuits, Caltech, 1990.
95P. Butkovič.

Max-algebra: the linear algebra of combinatorics?, in: Linear Algebra and Appl., 2003, vol. 367, p. 313-335.
96P. Butkovič, H. Schneider, S. Sergeev.

Generators, extremals and bases of max cones, in: Linear Algebra Appl., 2007, vol. 421, n^o 2-3, p. 394–406.
97Z. Cao, K. Kim, F. Roush.

Incline algebra and applications, Ellis Horwood, 1984.
98J. Chaloupka.

Algorithms for Mean-Payoff and Energy Games, Masaryk University, Faculty of Informatics, 2011.
99C.-S. Chang.

Performance guarantees in Communication networks, Springer, 2000.
100W. Chou, R. Griffiths.

Ground states of one dimensional systems using effective potentials, in: Phys. Rev. B, 1986, vol. 34, p. 6219–34.
101P. Chretienne.

Les Réseaux de Petri Temporisés, Thèse Université Pierre et Marie Curie (Paris VI), Paris, 1983.
102J. Cochet-Terrasson.

Algorithmes d'itération sur les politiques pour les applications monotones contractantes, École des Mines, Dec. 2001.
103J. 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, p. 377–382.
104J. 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.
105G. 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, n^o 191.

http://hal.inria.fr/inria-00076367
106J.-P. Comet.

Application of max-plus algebra to biological sequence comparison, in: Theor. Comput. Sci., Special issue on max-plus algebras, 2003, vol. 293, p. 189–217.
107A. 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, p. 462–475.
108P. 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, p. 238–252.
109P. Cousot, R. Cousot.

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

Some relations between non expansive and order preserving maps, in: Proceedings of the AMS, 1980, vol. 78, n^o 3, p. 385–390.
111R. Cuninghame-Green.

Minimax Algebra, Lecture notes in Economics and Mathematical Systems, Springer, 1979, n^o 166.
112P. Del Moral.

Maslov optimization theory: topological aspects, in: Idempotency (Bristol, 1994), Cambridge, Publ. Newton Inst., Cambridge Univ. Press, Cambridge, 1998, vol. 11, p. 354–382.
113P. Del Moral, T. Thuillet, G. Rigal, G. Salut.

Optimal versus random processes : the nonlinear case, LAAS, 1990.
114M. Develin, B. Sturmfels.

Tropical convexity, in: Doc. Math., 2004, vol. 9, p. 1–27 (electronic).
115V. 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
116M. 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, p. 5606-5628.

http://arxiv.org/abs/0901.2915, http://hal.archives-ouvertes.fr/hal-00411243/en/
117M. 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.
118A. Elmasry.

Computing the subset partial order for dense families of sets, in: Information Processing Letters, 2009, vol. 109, n^o 18, p. 1082 - 1086.
119N. 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.
120A. Fathi.

Solutions KAM faibles et théorie de Mather sur les systèmes lagrangiens, in: C. R. Acad. Sci. Paris, Sér. I Math., 1997, vol. 324, n^o 9, p. 1043–1046.
121S. Fomin, A. Zelevinsky.

Cluster algebras. I. Foundations, in: J. Amer. Math. Soc., 2002, vol. 15, n^o 2, p. 497–529 (electronic).

http://arxiv.org/abs/math.RT/0104151
122S. Gaubert.

Performance Evaluation of (max,+) Automata, in: IEEE Trans. on Automatic Control, Dec 1995, vol. 40, n^o 12, p. 2014–2025.
123S. 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, p. 237–252.

http://dx.doi.org/10.1007/978-3-540-71316-6_17
124S. Gaubert, J. Gunawardena.

The Duality Theorem for min-max functions, in: C. R. Acad. Sci. Paris., 1998, vol. 326, Série I, p. 43–48.
125S. Gaubert, R. Katz.

The Minkowski Theorem for Max-plus Convex Sets, in: Linear Algebra and Appl., 2007, vol. 421, p. 356–369.

http://www.arxiv.org/abs/math.GM/0605078
126S. Gaubert, J. Mairesse.

Modeling and analysis of timed Petri nets using heaps of pieces, in: IEEE Trans. Automat. Control, 1999, vol. 44, n^o 4, p. 683–697.
127S. Gaubert, S. Sergeev.

The level set method for the two-sided eigenproblem, 2010, Preprint. Submitted.

http://arxiv.org/abs/1006.5702
128E. Gawrilow, M. Joswig.

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