Team, Visitors, External Collaborators
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
XML PDF e-pub
PDF e-Pub


Bibliography

Major publications by the team in recent years
[1]
M. 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
[2]
M. 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
[3]
M. 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
[4]
M. Akian, S. Gaubert, C. Walsh.
The max-plus Martin boundary, in: Doc. Math., 2009, vol. 14, pp. 195–240.
[5]
X. 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.
[6]
X. Allamigeon, P. Benchimol, S. Gaubert, M. Joswig.
Log-barrier interior point methods are not strongly polynomial, in: SIAM Journal on Applied Algebra and Geometry, 2018, vol. 2, no 1, pp. 140-178, https://arxiv.org/abs/1708.01544 - This paper supersedes arXiv:1405.4161. 31 pages, 5 figures, 1 table. [ DOI : 10.1137/17M1142132 ]
https://hal.inria.fr/hal-01674959
[7]
X. 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, Best paper award. The extended version of this conference article appeared in ACM Trans. Embed. Comput. Syst., 15(4):69:1–69:20, September 2016.
[8]
J. 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
[9]
S. Friedland, S. Gaubert, L. Han.
Perron-Frobenius theorem for nonnegative multilinear forms and extensions, in: Linear Algebra and its Applications, 2013, vol. 438, no 2, pp. 738–749, This paper was included in a list of “10 Notable Papers from the journal Linear Algebra & Its Applications over the last 50 years” at the occasion of the golden anniversary of the journal, celebrated in 2018..
http://dx.doi.org/10.1016/j.laa.2011.02.042
[10]
S. 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
[11]
S. 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
[12]
C. 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

Articles in International Peer-Reviewed Journals

[13]
M. Akian, S. Gaubert, J. Grand-Clément, J. Guillaud.
The operator approach to entropy games, in: Theory of Computing Systems, 2019, https://arxiv.org/abs/1904.05151, forthcoming. [ DOI : 10.1007/s00224-019-09925-z ]
https://hal.archives-ouvertes.fr/hal-02143807
[14]
M. Akian, S. Gaubert, A. Hochart.
A game theory approach to the existence and uniqueness of nonlinear Perron-Frobenius eigenvectors, in: Discrete and Continuous Dynamical Systems - Series A, 2020, vol. 40, pp. 207–231, https://arxiv.org/abs/1812.09871. [ DOI : 10.3934/dcds.2020009 ]
https://hal.inria.fr/hal-01967495
[15]
X. Allamigeon, S. Gaubert, M. Skomra.
The tropical analogue of the Helton–Nie conjecture is true, in: Journal of Symbolic Computation, March 2019, vol. 91, pp. 129-148, https://arxiv.org/abs/1801.02089 - The present results were announced in the conference MEGA2017 (INTERNATIONAL CONFERENCE ON EFFECTIVE METHODS IN ALGEBRAIC GEOMETRY, Université Nice Sophia Antipolis, June 2017, https://mega2017.inria.fr/). [ DOI : 10.1016/j.jsc.2018.06.017 ]
https://hal.inria.fr/hal-01674497
[16]
X. Allamigeon, R. D. Katz.
A Formalization of Convex Polyhedra Based on the Simplex Method, in: Journal of Automated Reasoning, August 2019, vol. 63, no 2, pp. 323–345. [ DOI : 10.1007/s10817-018-9477-1 ]
https://hal.archives-ouvertes.fr/hal-01967575
[17]
R. Bhatia, S. Gaubert, T. Jain.
Matrix versions of the Hellinger distance, in: Letters in Mathematical Physics, 2019, vol. 109, pp. 1777-1804, https://arxiv.org/abs/1901.01378. [ DOI : 10.1007/s11005-019-01156-0 ]
https://hal.inria.fr/hal-01973935
[18]
V. Boeuf, P. Robert.
A Stochastic Analysis of a Network with Two Levels of Service, in: Queueing Systems, August 2019, vol. 92, no 3-4, 30 p, https://arxiv.org/abs/1708.09590, forthcoming. [ DOI : 10.1007/s11134-019-09617-y ]
https://hal.archives-ouvertes.fr/hal-01583704
[19]
G. C. Calafiore, S. Gaubert, C. Possieri.
Log-sum-exp neural networks and posynomial models for convex and log-log-convex data, in: IEEE Transactions on Neural Networks and Learning Systems, 2019, https://arxiv.org/abs/1806.07850. [ DOI : 10.1109/TNNLS.2019.2910417 ]
https://hal.inria.fr/hal-01969634
[20]
S. Gaubert, M. MacCaig.
Approximating the Volume of Tropical Polytopes is Difficult, in: International Journal of Algebra and Computation, 2019, vol. 29, no 02, pp. 357–389, https://arxiv.org/abs/1706.06467. [ DOI : 10.1142/S0218196718500686 ]
https://hal.inria.fr/hal-01675715
[21]
S. Gaubert, N. Stott.
A convergent hierarchy of non-linear eigenproblems to compute the joint spectral radius of nonnegative matrices, in: Mathematical Control and Related Fields, 2019, https://arxiv.org/abs/1805.03284 - 18 pages. [ DOI : 10.3934/mcrf.2020011 ]
https://hal.inria.fr/hal-01967552
[22]
E. Goubault, A. Sagnier, M. Färber.
Directed topological complexity, in: Journal of Applied and Computational Topology, August 2019.
https://hal.archives-ouvertes.fr/hal-02434377
[23]
H. Le Cadre, P. Jacquot, C. Wan, C. Alasseur.
Peer-to-Peer Electricity Market Analysis: From Variational to Generalized Nash Equilibrium, in: European Journal of Operational Research, 2019, https://arxiv.org/abs/1812.02301, forthcoming. [ DOI : 10.1016/j.ejor.2019.09.035 ]
https://hal.archives-ouvertes.fr/hal-01944644

International Conferences with Proceedings

[24]
M. Akian, J.-P. Chancelier, B. Tran.
A Min-plus-SDDP Algorithm for Deterministic Multistage Convex Programming, in: 58th IEEE Conference on Decision and Control, Nice, France, December 2019.
https://hal.inria.fr/hal-02436343
[25]
M. Akian, S. Gaubert, Z. Qu, O. Saadi.
Solving Ergodic Markov Decision Processes and Perfect Information Zero-sum Stochastic Games by Variance Reduced Deflated Value Iteration, in: CDC 2019 - 58th IEEE Conference on Decision and Control, Nice, France, Proc. of the 58th IEEE Conference on Decision and Control, December 2019, https://arxiv.org/abs/1909.06185.
https://hal.inria.fr/hal-02423846
[26]
P. Jacquot, O. Beaude, P. Benchimol, S. Gaubert, N. Oudjane.
A Privacy-preserving Disaggregation Algorithm for Non-intrusive Management of Flexible Energy, in: CDC 2019 - 58th IEEE Conference on Decision and Control, Nice, France, Proceedings of the 58th IEEE Conference on Decision and Control, IEEE, December 2019, https://arxiv.org/abs/1903.03053.
https://hal.archives-ouvertes.fr/hal-02150209

Scientific Books (or Scientific Book chapters)

[27]
M. Akian, 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, W. McEneaney (editors), INDAM Series, Springer, February 2019, vol. 29, pp. 183–209, https://arxiv.org/abs/1801.01780.
https://hal.inria.fr/hal-01675068

Other Publications

[28]
O. Beaude, P. Benchimol, S. Gaubert, P. Jacquot, N. Oudjane.
A Privacy-preserving Method to Optimize Distributed Resource Allocation, August 2019, https://arxiv.org/abs/1908.03080 - working paper or preprint.
https://hal.archives-ouvertes.fr/hal-02262271
[29]
G. C. Calafiore, S. Gaubert, C. Possieri.
A Universal Approximation Result for Difference of log-sum-exp Neural Networks, December 2019, https://arxiv.org/abs/1905.08503 - working paper or preprint.
https://hal.inria.fr/hal-02423871
[30]
S. Friedland, S. Gaubert.
Spectral inequalities for nonnegative tensors and their tropical analogues, September 2019, https://arxiv.org/abs/1804.00204 - working paper or preprint.
https://hal.inria.fr/hal-01969021
[31]
S. Gaubert, A. Niv.
Tropical planar networks, December 2019, https://arxiv.org/abs/1910.12934 - working paper or preprint.
https://hal.inria.fr/hal-02423904
[32]
P. Jacquot, C. Wan, O. Beaude, N. Oudjane.
Efficient Estimation of Equilibria in Large Aggregative Games with Coupling Constraints, November 2019, https://arxiv.org/abs/1911.10571 - working paper or preprint.
https://hal.archives-ouvertes.fr/hal-01904546
[33]
P. Jacquot, C. Wan.
Nonatomic Aggregative Games with Infinitely Many Types, June 2019, https://arxiv.org/abs/1906.01986 - working paper or preprint.
https://hal.archives-ouvertes.fr/hal-02146294
[34]
C. Walsh.
Order isomorphisms of complete order-unit spaces, December 2019, working paper or preprint.
https://hal.archives-ouvertes.fr/hal-02425988
References in notes
[35]
M. Akian, J.-P. Chancelier, B. Tran.
A stochastic algorithm for deterministic multistage optimization problems, December 2018, https://arxiv.org/abs/1810.12870 - working paper or preprint.
https://hal.inria.fr/hal-01964189
[36]
M. 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
[37]
M. Akian, 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, D. Kalise, K. Kunisch, Z. Rao (editors), De Gruyter, August 2018, https://arxiv.org/abs/1709.09049.
https://hal.inria.fr/hal-01675067
[38]
M. 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
[39]
M. Akian, S. Gaubert.
Policy iteration for perfect information stochastic mean payoff games with bounded first return times is strongly polynomial, 2013, Preprint arXiv:1310.4953, 17 pages.
http://hal.inria.fr/hal-00881207
[40]
M. 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
[41]
M. Akian, S. Gaubert, A. Hochart.
Generic uniqueness of the bias vector of finite stochastic games with perfect information, in: Journal of Mathematical Analysis and Applications, 2018, vol. 457, pp. 1038-1064, https://arxiv.org/abs/1610.09651. [ DOI : 10.1016/j.jmaa.2017.07.017 ]
https://hal.inria.fr/hal-01425543
[42]
M. 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
[43]
X. 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
[44]
X. 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
[45]
X. Allamigeon, P. Benchimol, S. Gaubert, M. Joswig.
Log-barrier interior point methods are not strongly polynomial, in: SIAM Journal on Applied Algebra and Geometry, 2018, vol. 2, no 1, pp. 140-178, https://arxiv.org/abs/1708.01544 - This paper supersedes arXiv:1405.4161. 31 pages, 5 figures, 1 table. [ DOI : 10.1137/17M1142132 ]
https://hal.inria.fr/hal-01674959
[46]
X. 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
[47]
X. Allamigeon, V. Boeuf, S. Gaubert.
Stationary solutions of discrete and continuous Petri nets with priorities, in: Performance Evaluation, August 2017, vol. 113, pp. 1 - 12, https://arxiv.org/abs/1612.07661. [ DOI : 10.1016/j.peva.2017.04.007 ]
https://hal.inria.fr/hal-01674492
[48]
X. 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
[49]
X. 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
[50]
X. Allamigeon, S. Gaubert, R. Katz, M. Skomra.
Condition numbers of stochastic mean payoff games and what they say about nonarchimedean semidefinite programming, in: 23rd International Symposium on Mathematical Theory of Networks and Systems, Hong-Kong, France, July 2018, https://arxiv.org/abs/1802.07712 - 14 pages, 2 figures.
https://hal.inria.fr/hal-01967555
[51]
X. 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
[52]
X. Allamigeon, S. Gaubert, M. Skomra.
Tropical spectrahedra, October 2016, arXiv:1610.06746.
https://hal.inria.fr/hal-01422639
[53]
X. Allamigeon, S. Gaubert, M. Skomra.
Solving generic nonarchimedean semidefinite programs using stochastic game algorithms, in: Journal of Symbolic Computation, 2018, vol. 85, pp. 25-54, An abridged version of this article appeared in the proceedings of ISSAC 2016. [ DOI : 10.1016/j.jsc.2017.07.002 ]
https://hal.inria.fr/hal-01674494
[54]
X. Allamigeon, R. D. Katz.
A Formalization of Convex Polyhedra Based on the Simplex Method, in: Journal of Automated Reasoning, August 2018.
https://hal.archives-ouvertes.fr/hal-01967575
[55]
P. Andy, W. Faisal, F. Bonnans.
MIDAS: A Mixed Integer Dynamic Approximation Scheme, Inria, 2016.
https://hal.inria.fr/hal-01401950
[56]
F. Baccelli, G. Cohen, G.-J. Olsder, J.-P. Quadrat.
Synchronization and linearity: an algebra for discrete event systems, Wiley, 1992.
[57]
G. 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
[58]
R. Bhatia, S. Gaubert, T. Jain.
Matrix versions of the Hellinger distance, 2019, To appear in Letters in Math. Physics.
[59]
V. Boeuf, P. Robert.
A Stochastic Analysis of a Network with Two Levels of Service, August 2017, working paper or preprint.
https://hal.archives-ouvertes.fr/hal-01583704
[60]
F. Bonnans, S. Gaubert.
Recherche opérationnelle. Aspects mathématiques et applications, Ellipse, March 2016, 391 p.
https://hal.inria.fr/hal-01422645
[61]
P. Butkovič.
Max-algebra: the linear algebra of combinatorics?, in: Linear Algebra and its applications, 2003, vol. 367, pp. 313–335.
[62]
P. 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
[63]
J. 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.
[64]
G. 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.
[65]
A. Connes.
Trace formula in noncommutative geometry and the zeros of the Riemann zeta function, in: Selecta Math. (N.S.), 1999, vol. 5, no 1, pp. 29–106.
[66]
A. Connes, C. Consani.
The Arithmetic Site, in: Comptes Rendus Mathématiques, 2014, vol. Ser. I 352, pp. 971–975.
[67]
A. Connes, C. Consani.
Geometry of the arithmetic site, 2015, arXiv:1502.05580.
[68]
A. Connes, C. Consani.
Geometry of the arithmetic site, in: Adv. Math., 2016, vol. 291, pp. 274–329.
[69]
P. 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.
[70]
A. 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
[71]
M. Farber.
Invitation to Topological Robotics, Zurich lectures in advanced mathematics, European Mathematical Society, 2008.
[72]
A. 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
[73]
O. 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
[74]
W. 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.
[75]
S. 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
[76]
S. 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
[77]
S. 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
[78]
S. 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
[79]
S. Gaubert, A. Niv.
Tropical totally positive matrices, in: Journal of Algebra, December 2018, vol. 515, pp. 511-544, https://arxiv.org/abs/1606.00238 - arXiv:1606.00238. [ DOI : 10.1016/j.jalgebra.2018.07.005 ]
https://hal.inria.fr/hal-01423747
[80]
S. 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
[81]
T. 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
[82]
I. 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.
[83]
M. Grandis.
Directed Algebraic Topology, Models of non-reversible worlds, Cambridge University Press, 2009.
[84]
S. 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
[85]
B. 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.
[86]
H. 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
[87]
I. Itenberg, G. Mikhalkin, E. Shustin.
Tropical algebraic geometry, Oberwolfach Seminars, Birkhäuser Verlag, Basel, 2007, vol. 35, viii+103 p.
[88]
P. Jacquot, O. Beaude, S. Gaubert, N. Oudjane.
Demand Side Management in the Smart Grid: an Efficiency and Fairness Tradeoff, in: 7th IEEE International Conference on Innovative Smart Grid Technologies, Torino, France, August 2017, https://arxiv.org/abs/1711.11129.
https://hal.inria.fr/hal-01675658
[89]
P. Jacquot, S. Gaubert, N. Oudjane, O. Beaude, P. Benchimol.
Procédé de gestion décentralisée de consommation électrique non-intrusif, EDF and Inria, 2018, French Patent, FR1872553, filed to INPI on 7 Dec. 2018.
[90]
P. Jacquot.
Game theory and Optimization Methods for Decentralized Electric Systems, 2019.
[91]
P. Jacquot, C. Wan.
Nonsmooth Aggregative Games with Coupling Constraints and Infinitely Many Classes of Players, October 2018, https://arxiv.org/abs/1806.06230 - working paper or preprint.
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