Tropical Linear Regression and Mean Payoff Games: Or, How to Measure the Distance to Equilibria

Autor: Marianne Akian, Stéphane Gaubert, Yang Qi, Omar Saadi

Publikováno v: SIAM Journal on Discrete Mathematics. 37:632-674

We study a tropical linear regression problem consisting in finding the best approximation of a set of points by a tropical hyperplane. We establish a strong duality theorem, showing that the value of this problem coincides with the maximal radius of

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::67e40496d042f1b9ecb6380c7e48eedb
https://doi.org/10.1137/21m1428297

A game theory approach to the existence and uniqueness of nonlinear Perron-Frobenius eigenvectors

Autor: Stéphane Gaubert, Antoine Hochart, Marianne Akian

Publikováno v: Discrete and Continuous Dynamical Systems-Series A
Discrete and Continuous Dynamical Systems-Series A, American Institute of Mathematical Sciences, 2020, 40, pp.207--231. ⟨10.3934/dcds.2020009⟩
Discrete and Continuous Dynamical Systems-Series A, 2020, 40, pp.207--231. ⟨10.3934/dcds.2020009⟩

We establish a generalized Perron-Frobenius theorem, based on a combinatorial criterion which entails the existence of an eigenvector for any nonlinear order-preserving and positively homogeneous map \begin{document}$ f $\end{document} acting on the

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::5eb619e6974966d36a204aa3ec22a3ee
https://hal.inria.fr/hal-01967495

A Min-plus-SDDP Algorithm for Deterministic Multistage Convex Programming

Autor: Jean-Philippe Chancelier, Benoît Tran, Marianne Akian

Publikováno v: CDC 2019-58th IEEE Conference on Decision and Control
CDC 2019-58th IEEE Conference on Decision and Control, Dec 2019, Nice, France
CDC

International audience; We consider discrete time optimal control problems with finite horizon involving continuous states and possibly both continuous and discrete controls, subject to non-stationary linear dynamics and convex costs. In this general

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::8092206c905a2f2559bf2edfceaa30c3
https://hal.inria.fr/hal-02436343

Tropical compound matrix identities

Autor: Marianne Akian, Stéphane Gaubert, Adi Niv

Publikováno v: Linear Algebra and its Applications
Linear Algebra and its Applications, Elsevier, 2018, 551, pp.162-206. ⟨10.1016/j.laa.2018.04.006⟩
Linear Algebra and its Applications, 2018, 551, pp.162-206. ⟨10.1016/j.laa.2018.04.006⟩

We prove identities on compound matrices in extended tropical semirings. Such identities include analogues to properties of conjugate matrices, powers of matrices and~$\adj(A)\det(A)^{ -1}$, all of which have implications on the eigenvalues of the co

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::7cb150f204ed8dc724b67901afe0592a
https://hal.inria.fr/hal-01469638

Probabilistic Max-Plus Schemes for Solving Hamilton-Jacobi-Bellman Equations

Autor: Marianne Akian, Eric Fodjo

Publikováno v: Springer INdAM Series ISBN: 9783030019587
Numerical Methods for Optimal Control Problems
M. Falcone; R. Ferretti; L. Grune; W. McEneaney. Numerical Methods for Optimal Control Problems, 29, Springer, pp.183-209, 2019, INDAM Series

We consider fully nonlinear Hamilton-Jacobi-Bellman equations associated to diffusion control problems involving a finite set-valued (or switching) control and possibly a continuum-valued control. In previous works (Akian and Fodjo, A probabilistic m

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::5da6610953e29047bc5240824e3b5fd1
https://doi.org/10.1007/978-3-030-01959-4_9