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.

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

11S. Detournay.

Multigrid methods for zero-sum two player stochastic games, École Polytechnique (France), September 2012.
12O. Fercoq.

Optimisation de vecteurs propres de Perron et applications : du référencement de pages web à la chronothérapie, École Polytechnique (France), September 2012.

http://pastel.archives-ouvertes.fr/pastel-00743187

Articles in International Peer-Reviewed Journals

13A. Adjé, S. Gaubert, E. Goubault.

Coupling policy iteration with semi-definite relaxation to compute accurate numerical invariants in static analysis, in: Log. Methods Comput. Sci., 2012, vol. 8, n^o 1, 1:01, 32 p. [ DOI : 10.2168/LMCS-8(1:1)2012 ]

http://arxiv.org/abs/1111.5223
14M. Akian, S. Detournay.

Multigrid methods for two-player zero-sum stochastic games, in: Numer. Linear Algebra Appl., 2012, vol. 19, n^o 2, p. 313–342. [ DOI : 10.1002/nla.1815 ]

http://arxiv.org/abs/1107.1653, http://hal.inria.fr/hal-00773036
15M. 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
16X. 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
17X. Allamigeon.

On the Complexity of Strongly Connected Components in Directed Hypergraphs, in: Algorithmica, 2013, To appear..

http://arxiv.org/abs/1112.1444
18F. 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
19E. Bouin, V. Calvez, N. Meunier, S. Mirrahimi, B. Perthame, G. Raoul, R. Voituriez.

Invasion fronts with variable motility: phenotype selection, spatial sorting and wave acceleration, in: Comptes Rendus Mathématiques, 2012, Accepted.

http://fr.arxiv.org/abs/1207.2355, http://hal.archives-ouvertes.fr/hal-00716349
20O. Fercoq, M. Akian, M. Bouhtou, S. Gaubert.

Ergodic Control and Polyhedral approaches to PageRank Optimization, in: IEEE TAC, 2013, vol. 58, n^o 1, p. 134–148, Published on line. [ DOI : 10.1109/TAC.2012.2226103 ]

http://arxiv.org/abs/1011.2348
21S. Friedland, S. Gaubert, L. Han.

Perron–Frobenius theorem for nonnegative multilinear forms and extensions, in: Linear Algebra Appl., 2013, vol. 438, n^o 2, p. 738–749. [ DOI : 10.1016/j.laa.2011.02.042 ]

http://arxiv.org/abs/0905.1626
22S. Gaubert, R. Katz, S. Sergeev.

Tropical linear-fractional programming and parametric mean payoff games, in: Journal of symbolic computation, 2012, vol. 47, p. 1447-1478, Special issue on invariant generation and advanced techniques for reasoning about loops.

http://arxiv.org/abs/1101.3431
23S. Gaubert, W. McEneaney.

Min-max spaces and complexity reduction in min-max expansions, in: Appl. Math. Optim., 2012, vol. 65, n^o 3, p. 315–348.

http://dx.doi.org/10.1007/s00245-011-9158-5
24S. Gaubert, S. Sergeev.

The level set method for the two-sided max-plus eigenproblem, in: J. Disc. Event Dyn. Syst., 2012, Published online 25 May 2012. [ DOI : 10.1007/s10626-012-0137-z ]

http://fr.arxiv.org/abs/1006.5702
25S. Gaubert, G. Vigeral.

A maximin characterization of the escape rate of non-expansive mappings in metrically convex spaces, in: Math. Proc. of Cambridge Phil. Soc., March 2012, vol. 152, n^o 2, p. 341-363. [ DOI : 10.1017/S0305004111000673 ]

http://arxiv.org/abs/1012.4765, http://hal.inria.fr/hal-00661863
26T. M. Gawlitza, H. Seidl, A. Adjé, S. Gaubert, E. Goubault.

Abstract interpretation meets convex optimization, in: J. Symbolic Comput., 2012, vol. 47, n^o 12, p. 1416–1446, Special issue on Invariant generation and reasoning about loops..

http://dx.doi.org/10.1016/j.jsc.2011.12.048
27S. Mirrahimi, G. Barles, B. Perthame, P. Souganidis.

Singular Hamilton-Jacobi equation for the tail problem, in: SIAM Journal on Mathematical Analysis, 2012, Accepted.

http://fr.arxiv.org/abs/1007.2802, http://hal.archives-ouvertes.fr/hal-00503154
28S. Mirrahimi.

Adaptation and migration of a population between patches, in: Discrete and Continuous Dynamical Systems Series B, 2012, Accepted.

http://fr.arxiv.org/abs/1204.0801, http://hal.archives-ouvertes.fr/hal-00684974
29S. Mirrahimi, G. Raoul.

Dynamics of sexual populations structured by a space variable and a phenotypical trait, in: Theoretical Population Biology, 2012, Accepted.

http://fr.arxiv.org/abs/1105.1936
30S. Mirrahimi, P. Souganidis.

A homogeneization approach for the motion of motor proteins, in: Nonlinear Differential Equations and Applications, 2012, Accepted.

http://fr.arxiv.org/abs/1201.3747, http://hal.archives-ouvertes.fr/hal-00660998
31P. Poncet.

Domain theory and mirror properties in inverse semigroups, in: Semigroup Forum, 2012, vol. 84, n^o 3, p. 434–446.

http://dx.doi.org/10.1007/s00233-012-9392-4

International Conferences with Proceedings

32M. Akian.

Fixed points of discrete convex monotone dynamical systems, in: Tropical and Indempotent Mathematics, Moscow, Russia, G. Litvinov, V. Maslov, A. Kushner, S. Sergeev (editors), August 2012.
33O. Fercoq.

PageRank optimization applied to spam detection, in: 6th International conference on NETwork Games, COntrol and OPtimization (Netgcoop), Avignon, France, November 2012.

http://fr.arxiv.org/abs/1203.1457
34C. Walsh.

Studying isometry groups using the horofunction boundary, in: Tropical and Indempotent Mathematics, Moscow, Russia, G. Litvinov, V. Maslov, A. Kushner, S. Sergeev (editors), August 2012.

Conferences without Proceedings

35M. Akian, S. Gaubert, R. Nussbaum.

Nonlinear spectral radii of order-preserving maps and infinite horizon zero-sum two-player stochastic games, in: MTNS 2012 (20th International Symposium on Mathematical Theory of Networks and Systems), Melbourne, Australia, July 2012.
36M. Akian, S. Gaubert, M. Sharify.

Tropical bounds for the eigenvalues of structured matrices, in: 2012 SIAM Conference on Applied Linear Algebra, Valencia, Spain, June 2012.
37X. Allamigeon, S. Gaubert, E. Goubault, R. Katz.

Minimal representations of tropical polyhedra by half-spaces, in: 2012 SIAM Conference on Applied Linear Algebra, Valencia, Spain, June 2012.
38O. Fercoq.

Optimization of the HOTS score of a website's pages, in: 2012 SIAM Conference on Applied Linear Algebra, Valencia, Spain, June 2012.

Scientific Books (or Scientific Book chapters)

39N. Beeker, S. Gaubert, C. Glusa, L. Liberti.

Is the Distance Geometry Problem in NP?, in: Distance Geometry: Theory, Methods, and Applications, A. Mucherino, et al. (editors), Springer, 2013.
40F. 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, 2012, p. 257-299, In Press.

http://hal.archives-ouvertes.fr/hal-00770366
41C. Walsh.

The horofunction boundary and isometry group of the Hilbert geometry, A. Papadopoulos (editor), 2012, To appear.

Internal Reports

42F. Bonnans, S. Gaubert.

Recherche opérationnelle: aspects mathématiques et applications, École Polytechnique, 2012, Huitième édition, 180 p..

Other Publications

43Definable zero-sum stochastic games, 2013, Submitted.

http://fr.arxiv.org/abs/1301.1967
44Markov operators on cones and non-commutative consensus, 2012, Submitted.
45M. 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
46M. Akian, S. Gaubert, R. Nussbaum.

Uniqueness of the fixed point of nonexpansive semidifferentiable maps, 2012, Submitted.

http://fr.arxiv.org/abs/1201.1536
47M. Akian, S. Gaubert, M. Sharify.

Log-majorization of the moduli of the eigenvalues of a matrix polynomial by tropical roots, 2012, Preprint.
48X. Allamigeon, R. Katz.

Minimal external representations of tropical polyhedra, 2012.

http://fr.arxiv.org/abs/1205.6314
49J. Clairambault, O. Fercoq.

Physiologically structured cell population dynamic models with applications to combined drug delivery optimisation in oncology, 2012.

http://hal.archives-ouvertes.fr/hal-00750633
50O. Fercoq.

Convergence of Tomlin's HOTS algorithm, 2012.

http://fr.arxiv.org/abs/1205.6727
51S. Gaubert, Z. Qu.

The contraction rate in Thompson metric of order-preserving flows on a cone - application to generalized Riccati equations, 2012.

http://fr.arxiv.org/abs/1206.0448
52S. Mirrahimi, B. Perthame, J. Wakano.

Direct competition results from strong competition for limited resource, 2012, Submitted.

http://fr.arxiv.org/abs/1201.5826, http://hal.archives-ouvertes.fr/hal-00663832
53P. Poncet.

Convexities on ordered structures have their Krein–Milman theorem, 2012, Submitted.
54P. Poncet.

How regular can maxitive measures be?, 2012, Submitted to Topology and its Applications.
55C. Walsh.

The asymptotic geometry of the Teichmüller metric, 2012.

http://fr.arxiv.org/abs/1210.5565

References in notes

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Perturbation of eigenvalues of matrix pencils and optimal assignment problem, in: C. R. Acad. Sci. Paris, Série I, 2004, vol. 339, p. 103–108.

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59M. Akian, R. Bapat, S. Gaubert.

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

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60M. Akian, R. Bapat, S. Gaubert.

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http://hal.inria.fr/inria-00073240
61M. 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
62M. 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/
63M. 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
64M. 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
65M. Akian, J. Menaldi, A. Sulem.

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Duality between probability and optimization, in: Idempotency, J. Gunawardena (editor), Publications of the Isaac Newton Institute, Cambridge University Press, 1998.
67X. 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.
68X. 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
69X. 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 ]

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70N. Bacaër.

Perturbations singulières et théorie spectrale min-plus, Université Paris 6, January 2002.
71F. 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.
72R. Bapat.

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74R. 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..
75A. 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.
76A. Berenstein, A. N. Kirillov.

The Robinson-Schensted-Knuth bijection, quantum matrices, and piece-wise linear combinatorics, in: Proceedings of FPSAC'01, 2001.
77F. 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
78T. Blyth, M. Janowitz.

Residuation Theory, Pergamon press, 1972.
79H. Braker.

Algorithms and Applications in Timed Discrete Event Systems, Delft University of Technology, Dec 1993.
80S. Burns.

Performance analysis and optimization of asynchronous circuits, Caltech, 1990.
81P. Butkovič.

Max-algebra: the linear algebra of combinatorics?, in: Linear Algebra and Appl., 2003, vol. 367, p. 313-335.
82Z. Cao, K. Kim, F. Roush.

Incline algebra and applications, Ellis Horwood, 1984.
83C.-S. Chang.

Performance guarantees in Communication networks, Springer, 2000.
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85P. Chretienne.

Les Réseaux de Petri Temporisés, Thèse Université Pierre et Marie Curie (Paris VI), Paris, 1983.
86J. Cochet-Terrasson.

Algorithmes d'itération sur les politiques pour les applications monotones contractantes, École des Mines, Dec. 2001.
87J. 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.
88J. 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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90J.-P. Comet.

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91A. 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.
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Tropical polytopes and cellular resolutions, in: Experimental Mathematics, 2007, vol. 16, n^o 3, p. 277–292.

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100V. Dhingra, S. Gaubert.

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101M. 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/
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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.
105A. Fathi.

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Perron vector optimization applied to search engines, 2011.

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

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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
115S. Gaubert, M. Sharify.

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http://dx.doi.org/10.1007/978-3-642-02894-6_28, http://arxiv.org/abs/0905.0121
116S. 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
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