Max Plus1,
L'algèbre (max,+) et sa symétrisation ou l'algèbre
des équilibres.
C. R. Acad. Sci. Paris, t. 311, Série II, 1990.
M.Akian, J.L. Menaldi, and A.Sulem,
Multi-asset portfolio selection problem with transaction costs.
Probabilités numériques (Paris, 1992).
Mathematics and Computers in Simulation 38, 1995, 163-172.
M.Akian, J.L. Menaldi, and A.Sulem,
On an investement-consumption model with transaction costs.
SIAM Journal of Control and Optimization 34, no. 1, 1996, 329-364.
Abstract.
Preliminary version in
postscript form.
J.P. Quadrat and Max-Plus Working group2,
Min-plus linearity and Statistical Mechanics.
Markov Processes and Related fields, 3, nb 4, 1997, 565-587.
M. Akian, R. Bapat, and S. Gaubert,
Asymptotics of the Perron eigenvalue and eigenvector using max-algebra.
C. R. Acad. Sci. Paris, t. 327, Série I, 1998, 927-932.
Preliminary version in the
INRIA research report 3450.
M. Akian and P.-A. Bliman,
On super-high frequencies in discontinuous 1st-order delay-differential
equations.
Journal of Differential Equations, 162, 2000, 326-358.
Preliminary version in the
INRIA research report 3443.
M. Akian, A. Sulem, and M. Taksar,
Dynamic optimisation of long term growth rate for a portfolio with
transaction costs and logarithmic utility .
Mathematical Finance, 11(2), 2001, 153-188.
pdf.
M. Akian and S. Bismuth,
Instability of rapidly-oscillating periodic solutions for
discontinuous differential delay equations.
Differential and Integral Equations, 15(1), 2002, 53-90.
postscript,
pdf.
M. Akian, P.-A. Bliman, and M. Sorine,
Control of delay systems with relay.
IMA Journal on Mathematical Control and Information,
Special issue on Analysis and Design of Delay and Propagation Systems
, 19, 2002,133-155.
Abstract.
M. Akian, S. Gaubert, and V. Kolokoltsov.
Invertibility of Functional Galois Connections.
Comptes Rendus Mathématique 335(11), 2002, 883--888.
doi:10.1016/S1631-073X(02)02594-3.
M. Akian and I. Singer.
Topologies on lattice ordered groups, separation from closed downward sets and conjugations of type Lau.
Optimization. 52(6), 2003, 629--672.
doi:10.1080/02331930310001637396.
Preliminary version in postscript form.
M. Akian, S. Gaubert, B. Lemmens and R. Nussbaum.
Iteration of order preserving subhomogeneous maps on a cone.
Mathematical Proceedings of the Cambridge Philosophical Society 140(1), 2006, 157-176.
doi:10.1017/S0305004105008832.
Preliminary version in
arXiv:math.DS/0410084.
M. Akian, S. Gaubert, and A. Lakhoua.
The max-plus finite element method for solving deterministic optimal control problems: basic properties and convergence analysis.
SIAM Journal on Control and Optimization, 47, no. 2, 2008, 817--848.
Preliminary version in
arXiv:math.OC/0603619,
2006.
M. Akian, B. David, and S. Gaubert.
Un théorème de représentation des solutions de
viscosité d'une équation d'Hamilton-Jacobi-Bellman ergodique
dégénérée sur le tore.
C. R. Acad. Sci. Paris, Ser. I, 346:1149-1154, 2008.
M. Akian, S. Gaubert, and C. Walsh.
The max-plus Martin boundary.
Documenta Mathematica, 14, 2009, 195--240.
Preliminary version in the INRIA research report 5429 and
arXiv:math.MG/0412408.
M. Akian, S. Gaubert, and B. Lemmens.
Stability and convergence in discrete convex monotone dynamical
systems.
Journal of Fixed Point Theory and Applications, 9(2), 2011, 295--325.
Preliminary version in
arXiv:1003.5346.
M. Akian, S. Gaubert, V. Nitica, and I. Singer.
Best approximation in max-plus semimodules.
Linear Algebra and its Applications, 435(12), 2011, 3261--3296.
Preliminary version in
arXiv:1012.5492.
M. Akian, S. Gaubert, and A. Guterman.
Tropical polyhedra are equivalent to mean payoff games.
Internat. J. Algebra Comput., 22(1), 2012, 1250001, 43.
Preliminary version in
arXiv:0912.2462.
M. Akian and S. Detournay.
Multigrid methods for two-player zero-sum stochastic games.
Numer. Linear Algebra Appl., 19(2), 2012, 313--342.
Preliminary version in
arXiv:1107.1653.
O. Fercoq, M. Akian, M. Bouhtou, and S. Gaubert.
Ergodic control and polyhedral approaches to pagerank optimization.
IEEE TAC, 58(1), 2013, 134--148.
Preliminary version in
arXiv:1011.2348.
M. Akian, S. Gaubert, and A. Marchesini.
Tropical bounds for eigenvalues of matrices.
Linear Algebra and its Applications, 446, 2014, 281--303.
Journal article. Preliminary version in
arXiv:1309.7319.
M. Akian, S. Gaubert, and A. Hochart.
Ergodicity conditions for zero-sum games.
Discrete and Continuous Dynamical Systems - Series A,
35(9):31, 2015. Preliminary version in
arXiv:1405.4658.
M. Akian, S. Gaubert, and R. Nussbaum.
Uniqueness of the fixed point of nonexpansive semidifferentiable maps.
Transactions of the American Mathematical Society, 368(2), 2016.
Preliminary version in
arXiv:1201.1536.
M. Akian, S. Gaubert, and R. Bapat.
Non-archimedean valuations of eigenvalues of matrix polynomials.
Linear Algebra and its Applications, 498:592--627, 2016.
Preliminary version in
arXiv:1601.00438.
M. Akian, S. Gaubert, and M. Sharify.
Log-majorization of the moduli of the eigenvalues of a matrix
polynomial by tropical roots.
Linear Algebra and its Applications, 528:394--435, 2017.
Preliminary version in
arXiv:1304.2967.
M. Akian, S. Gaubert, and A. Hochart.
Minimax representation of nonexpansive functions and application to
zero-sum recursive games.
Journal of Convex Analysis, 25(1), 2018.
Preliminary version in
arXiv:1605.04518, 2016.
M. Akian, S. Gaubert, and A. Niv.
Tropical compound matrix identities.
Linear Algebra and its Applications, 551:162--206, 2018.
Preliminary version in
arXiv:1702.00980, 2017.
M. Akian, S. Gaubert, and A. Hochart.
Generic uniqueness of the bias vector of finite stochastic games
with perfect information.
Journal of Mathematical Analysis and Applications, 457:1038--1064, 2018.
Preliminary version in
arXiv:1610.09651, 2016.
M. Akian, S. Gaubert, J. Grand-Clément, and J.Guillaud.
The operator approach to entropy games.
Theory of Computing Systems, 63:1089--1130, 2019.
Preliminary version in
arXiv:1904.05151, 2019.
M. Akian, S. Gaubert, and A. Hochart.
A game theory approach to the existence and uniqueness of nonlinear
perron-frobenius eigenvectors.
Discrete and Continuous Dynamical Systems - Series A, 40:207--231, 2020.
Preliminary version in
arXiv:1812.09871, 2020.
S. Gaubert, M. Akian, X. Allamigeon, M. Boyet, B.
Colin, T. Grohens, L. Massoulié, D.P. Parsons, F.
Adnet, É. Chanzy, L. Goix, F. Lapostolle, É.
Lecarpentier, C. Leroy, T. Loeb, J.-S. Marx, C. Télion,
L. Treluyer, P. Carli.
Understanding and monitoring the evolution of the covid-19 epidemic
from medical emergency calls: the example of the paris area.
Comptes Rendus Mathématique, 358(7):843--875, 2020.
Preliminary version in
arXiv:2005.14186, 2020.
M. Akian, S. Gaubert, Z. Qu, and O. Saadi.
Multiply accelerated value iteration for non-symmetric affine fixed
point problems and application to markov decision processes.
Accepted for publication in SIMAX.
Preliminary version in
arXiv:2009.10427, 2021.
Articles published in books or book chapters:
M. Akian,
Résolution numérique d'équations
d'Hamilton-Jacobi-Bellman au moyen d'algorithmes multigrilles
et d'itérations sur les politiques.
In Analysis and optimisation of systems.
Lecture notes in control and information sciences, vol. 111, Springer Verlag, 1988.
M. Akian,
Analyse de l'algorithme multigrille FMGH de résolution
d'équations d'Hamilton-Jacobi-Bellman.
In Analysis and optimisation of systems.
Lecture notes in control and information sciences, vol. 144, Springer Verlag, 1990.
M. Akian, J.P. Quadrat, and M. Viot,
Bellman processes.
In 11th International Conference on Analysis and Optimization
of Systems : Discrete Event Systems.
Lecture notes in control and information sciences, vol. 199,
Springer Verlag, 1994.
S. Gaubert, and Max Plus3,
Methods and Applications of (max,+) linear Algebra,
In STACS 97 (Lubeck).
Lecture Notes in Comput. Sci., vol. 1200, pp. 261--282.
Springer, Berlin, 1997.
Preliminary version in the
INRIA reseach report 3088.
M. Akian, J.P. Quadrat, and M. Viot,
Duality between probability and optimization.
In Idempotency (J. Gunawardena, ed.).
Publication of the Isaac Newton Institute, Crambridge University press, 1998. postscript, pdf.
M. Akian, S. Gaubert, and V. Kolokoltsov.
Set coverings and invertibility of Functional Galois Connections.
In Idempotent Mathematics and Mathematical Physics
(G.L. Litvinov and V.P. Maslov, eds.).
Series Contemporary Mathematics, Vol. 377, American Mathematical
Society. Providence, RI, 2005. pp. 19--51.
Preliminary version in ESI Preprint 1447
and in arXiv:math.FA/0403441.
M. Akian, S. Gaubert, and C. Walsh.
Discrete max-plus spectral theory.
In Idempotent Mathematics and Mathematical Physics
(G.L. Litvinov and V.P. Maslov, eds.).
Series Contemporary Mathematics, Vol. 377, American Mathematical
Society. Providence, RI, 2005. pp. 53--77.
Preliminary version in ESI Preprint 1485
and in arXiv:math.SP/0405225.
M. Akian, R. Bapat, and S. Gaubert.
Max-plus algebras.
In Handbook of Linear Algebra (Discrete Mathematics
and Its Applications, Vol. 39)
(L. Hogben, ed.).
Chapman & Hall/CRC, 2006.
M. Akian, S. Gaubert, and N. Ninove,
The T-PageRank: a model of self-validating effects of web surfing.
In Positive Systems.
Lecture notes in control and information sciences, vol. 341,
Springer Verlag, 2006, pp. 239--246.
M. Akian, S. Gaubert, and A. Guterman.
Linear independence over tropical semirings and beyond.
In Proceedings of the International Conference on Tropical and Idempotent Mathematics (G.L. Litvinov and S.N. Sergeev, eds.).
Series Contemporary Mathematics. Vol. 495, American Mathematical
Society. Providence, RI, 2009. pp. 1--38.
Preliminary version in arXiv:0812.3496.
M. Akian, S. Gaubert, and V. Kolokoltsov.
The optimal assignment problem for a countable state space.
In Proceedings of the International Conference on Tropical and Idempotent Mathematics (G.L. Litvinov and S.N. Sergeev, eds.).
Series Contemporary Mathematics. Vol. 495,
American Mathematical Society. Providence, RI, 2009. pp. 39--60.
Preliminary version in arXiv:0812.4866.
M. Akian, S. Gaubert, and A. Guterman.
Tropical Cramer determinants revisited.
In Tropical and Idempotent Mathematics and Applications (G.L. Litvinov and S.N. Sergeev, eds.).
Series Contemporary Mathematics. Vol. 616, American Mathematical Society.
Providence, RI, 2014.
Preliminary version in arXiv:1309.6298, 2013.
M. Akian and E. Fodjo.
From a monotone probabilistic scheme to a probabilistic max-plus
algorithm for solving Hamilton-Jacobi-Bellman equations.
In Hamilton-Jacobi-Bellman Equations: Numerical Methods and Applications in
Optimal Control (Z. Rao D. Kalise, K. Kunisch, eds.).
Radon Ser. Comput. Appl. Math. Vol. 21, De Gruyter, 2018.
Preliminary version in arXiv:1709.09049, 2017.
M. Akian and E. Fodjo.
Probabilistic max-plus schemes for solving Hamilton-Jacobi-Bellman equations.
In Numerical Methods for Optimal Control Problems (M. Falcone, R. Ferretti, L. Grune, and W. McEneaney, eds.).
INDAM Series, Vol. 29, Springer, 2019, pp. 183--209.
Preliminary version in arXiv:1801.01780, 2018.
International conference proceedings:
M. Akian and A. Bensoussan,
On the stochastic Ramsey problem.
IEEE CDC, Athènes, Grèce, 1986.
M. Akian, J.P. Chancelier, and J.P. Quadrat,
Dynamic programming complexity and application.
IEEE CDC, Austin Texas, Dec. 1988.
Max Plus1,
Linear systems in (max, +) algebra.
Proceedings of the 29th Conference on Decision and Control, Honolulu, Hawaii, Dec. 1990. postscript, pdf.
M. Akian and A. Sulem,
Application of ``Pandore'', an expert system in stochastic control,
to portfolio selection problems.
In Artificial Intelligence, Expert Systems and Symbolic Computing,
North Holand (IMACS), 1992.
Max-Plus Working group3,
presented by Jean-Pierre Quadrat,
Max-plus algebra and applications to system theory and optimal
control.
Proceedings of the International Congress of Mathematicians,
Zürich, 1994. Birkhäuser, Basel, Switzerland 1995.
M. Akian, P. Séquier, A Sulem, and A. Aboulalaa,
A finite horizon portfolio selection problem with multi-risky
assets and transaction costs : the dynamic asset allocation example.
In Actes Association Française de Finance,
Bordeaux, Juin 1995.
M. Akian, P. Séquier, and A Sulem,
A finite horizon multidimensional portfolio selection problem
with singular transactions.
Proceedings of the 34th Conference on Decision and Control,
New Orléans, Dec. 1995, vol. 3, 2193-2198. pdf.
M. Akian, A Sulem, and M. Taksar,
Maximization of a long term growth rate for a mixed portfolio
with transaction costs.
Proceedings of the 17th IFIP Conference, Prague, Juillet 1995, 132-135.
M. Akian, J.P. Quadrat, and M. Viot,
Bellman processes with independent increments.
Proceedings of the 17th IFIP Conference, Prague, Juillet 1995, 207-210.
M. Akian and P.-A. Bliman,
On super-high-frequencies in discontinuous 1st-order
delay-differential equations.
In 6th IEEE Mediterranean Conference on Control and Systems,
Alghero, Italy, June 9-11, 1998.
M. Akian, P.-A. Bliman, and M. Sorine,
P.I. control of nonlinear oscillations for a system with delay.
In 8th IFAC LSS'98, Patras, Greece, July 15-17, 1998.
K. Blin, M. Akian, F. Bonnans, E. Hoffman, C. Martini, and K. Zeghal,
A stochastic conflict detection model revisited.
In Proceedings of AIAA GNC, Denver, August 2000.
K. Blin, M. Akian, F. Bonnans, E. Hoffman, and K. Zeghal,
A stochastic conflict detection method integrating planned heading and
velocity changes.
In Proceedings of the IEEE CDC, Sydney, Dec. 2000.
M. Akian and S. Gaubert,
A spectral theorem for convex monotone homogeneous maps.
In Proceedings of the Satellite Workshop on Max-Plus Algebras,
IFAC SSSC'01, Praha, 2001. Elsevier.
M. Akian, R. B. Bapat, and S. Gaubert,
Generic Asymptotics of Eigenvalues using Min-Plus Algebra.
In Proceedings of the Satellite Workshop on Max-Plus Algebras,
IFAC SSSC'01, Praha, 2001. Elsevier.
M. Akian, S. Gaubert, and A. Lakhoua.
A max-plus finite element method for solving finite horizon deterministic
optimal control problems.
In Proceedings of MTNS 2004.
Preliminary version in the INRIA research report 5163
and in arXiv:math.OC/0404184, 2004.
M. Akian, S. Gaubert, and A. Lakhoua.
The max-plus finite element method for optimal control problems:
further approximation results.
In Proceedings of the joint 44th IEEE Conference on Decision and
Control and European Control Conference ECC 2005 (CDC-ECC'05),
Seville, Spain, 2005.
Preliminary version in
arXiv:math.OC/0509250.
M. Akian, S. Gaubert, and V. N. 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, Spain, 2005.
Preliminary version in
arXiv:math.PR/0509279.
M. Akian, S. Gaubert, and C. Walsh.
How to find horizon-independent optimal strategies leading
off to infinity: a max-plus approach.
In Proc. of the 45th IEEE Conference on Decision and Control (CDC'06)
, San Diego, 2006.
Preliminary version in
arXiv:math.OC/0609243.
M. Akian.
Representation of stationnary solutions of
Hamilton-Jacobi-Bellman equations: a max-plus point of view.
In G .L. Litvinov, V. P. Maslov, and S. N. Sergeev, editors,
Proc. of the International Workshop ``Idempotent and Tropical Mathematics and
problems of Mathematical Physics'', Moscow, Aug. 25-30, 2007, volume 1,
pages 6--11.
M. Akian, S. Gaubert, and A. Lakhoua.
Convergence analysis of the max-plus finite element method for
solving deterministic optimal control problems.
In Proc. of the 47th IEEE Conference on Decision and Control (CDC'08), Cancun, 2008.
M. Akian, S. Gaubert, and A. Guterman.
The correspondence between tropical convexity and mean payoff games.
In Proceedings of the 19th International Symposium on
Mathematical Theory of Networks and Systems (MTNS 2010), 59 July, 2010,
Budapest, Hungary, pp. 1295--1302, 2010.
M. Akian.
Fixed points of discrete convex monotone dynamical systems.
In Tropical and Indempotent Mathematics (G.L. Litvinov, V.P. Maslov, A.G. Kushner, and S.N. Sergeev, eds), Moscow, Russia, August 2012.
M. Akian, J. Cochet-Terrasson, S. Detournay, and S. Gaubert.
Solving multichain stochastic games with mean payoff by policy
iteration.
In Proc. of the 52nd IEEE Conference on Decision and Control
(CDC'13), Florence, Italy, 2013.
M. Akian, S. Gaubert, and A. Hochart.
Generic uniqueness of the bias vector of mean payoff zero-sum games.
In 53rd IEEE Conference on Decision and Control, Los Angeles, 2014.
Preliminary version in
arXiv:1411.1211.
M. Akian, S. Gaubert, and 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, 2015.
Preliminary version in
arXiv:1510.05396.
M. Akian and 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, US, 2016.
M. Akian and E. Fodjo.
A probabilistic max-plus numerical method for solving stochastic
control problems.
In 55th Conference on Decision and Control (CDC 2016), Las Vegas, US, 2016.
Preliminary version in
arXiv:1605.02816.
J.B. Eytard, M. Akian, M. Bouhtou, and S. Gaubert.
A bilevel optimization model for load balancing in mobile networks through price incentives.
In WiOpt 2017 - 15th International Symposium on Modeling and
Optimization in Mobile, Ad Hoc, and Wireless Networks, pp. 1--8, Paris,
France, May 2017. IEEE.
M. Akian, S. Gaubert, J. Grand-Clément, and J. Guillaud.
The operator approach to entropy games.
In 34th International Symposium on Theoretical Aspects of
Computer Science (STACS 2017), Hannover, Germany, March 2017.
M. Akian, S. Gaubert, Z. Qu, and O. Saadi.
Solving Ergodic Markov Decision Processes and Perfect Information
Zero-sum Stochastic Games by Variance Reduced Deflated Value Iteration.
In Proc. of the 58th IEEE Conference on Decision and Control, Nice, France,
December 2019.
Preliminary version in
arXiv:1909.06185.
M. Akian, X. Allamigeon, M. Boyet, and S. Gaubert.
A convex programming approach to solve posynomial systems.
Volume 12097 of ICMS 2020 - International Congress on
Mathematical Software, Lecture Notes in Computer Science.
Preliminary version in
arXiv:2005.07124.
L.V. Pascal, M. Akian, S. Nicol, and I. Chades.
A universal 2-state n-action adaptive management solver.
Proceedings of the AAAI Conference on Artificial Intelligence,
volume 35, pages 14884--14892, May 2021.
https://ojs.aaai.org/index.php/AAAI/article/view/17747.
M. Akian, R. Bapat, and S. Gaubert.
Min-plus methods in eigenvalue perturbation theory and generalised
Lidskii-Vishik-Ljusternik theorem.arXiv:math.SP/0402090,
2004.
Preliminary version in the
INRIA research report 5104.
M. Akian, S. Gaubert, N. Ninove,
Multiple equilibria of nonhomogeneous Markov chains and
self-validating Web rankings.arXiv:0712.0469, 2007.
M. Akian, S. Gaubert, and R.D. Nussbaum.
A Collatz-Wielandt characterization of the spectral radius of
order-preserving homogeneous maps on cones.arXiv:1112.5968, 2011.
M. Akian, J. Cochet-Terrasson, S. Detournay, and S. Gaubert.
Policy iteration algorithm for zero-sum multichain stochastic games
with mean payoff and perfect information.arXiv:1208.0446, 2012.
M. Akian and S. Gaubert.
Policy iteration for perfect information stochastic mean payoff games
with bounded first return times is strongly polynomial.arXiv:1310.4953, 2013.
M. Akian, J.-P. Chancelier, and B. Tran.
A stochastic algorithm for deterministic multistage optimization problems.arXiv:1810.12870, 2018.
M. Akian, M. Bouhtou, J.-B. Eytard, and S. Gaubert.
A bilevel optimization model for load balancing in mobile networks through price incentives.arXiv:1901.02363, 2019.
M. Akian, L. Ganassali, S. Gaubert, and L. Massoulié.
Probabilistic and mean-field model of COVID-19 epidemics with user mobility and contact tracing.arXiv:2009.05304, 2020.
M. Akian, J.-P. Chancelier, and B. Tran.
Tropical dynamic programming for lipschitz multistage stochastic
programming.arXiv:2010.10619, 2020.
M. Akian, S. Gaubert, Y. Qi, and O. Saadi.
Tropical linear regression and mean payoff games: or, how to measure
the distance to equilibria.arXiv:2106.01930, 2021.
M. Akian, S. Gaubert, and S. Vannucci.
Ambitropical convexity: The geometry of fixed point sets of shapley
operators.arXiv:2108.07748, 2021.
Collective name given to a working group in Discrete Event Systems at
INRIA (Méta2 project) composed, at the time of the article, of M.
Akian, G. Cohen, S. Gaubert, R. Nikhoukhah and J.P. Quadrat.
