I am a PhD student in optimization, since september 2017, at the CERMICS, École des Ponts ParisTech and the CMAP, École Polytechnique under the supervision of Jean-Philippe Chancelier and Marianne Akian.

The dynamic programming approach applied to stochastic control problems allows one to find optimal feedback policies but it requires solving a nonlinear equation or a fully nonlinear partial differential equation of Hamilton-Jacobi type over the state space. Hence, this method suffers from the curse of dimensionality, for instance grid-based methods like finite-difference or finite element methods have a complexity exponential in the dimension of the state space.

Several methods were created to bypass this difficulty by assuming some structure on the problem. Examples are the max-plus based method of McEneaney and the stochastic dual dynamic programming (SDDP) algorithm of Pereira and Pinto.

We aim to associate and compare these methods in order to solve more general structures, namely problems involving a finite set-valued (or switching) control and a continuum-valued control, knowing that the value function associated to a fixed switching strategy is convex.

- We put in a common framework both a discrete time version of Zheng Qu's max-plus algorithm and a deterministic version of the SDDP algorithm. We studied the convergence of an algorithm in this general framework which is linked with the convergence of both the discrete time version of Zheng Qu's algorithm and the deterministic version of SDDP.

An early version of this work was presented at the SMAI-MODE 2018 conference (here is the poster) and at the ISMP 2018 conference. A preprint is available here.

- A stochastic algorithm for deterministic multistage optimization problems, with Marianne Akian and Jean-Philippe Chancelier, October 2018, arXiv preprint.

- Teaching assistant for a course on Discrete Mathematics by Igor Kortchemski, for the first year of the Bachelor program of the École Polytechnique.
- Tutor for a course on Operational Research by Stéphane Gaubert, for the third year (Master) students of the École Polytechnique.

I am a former student of Paris-Sud University. There I studied mathematics for several years, succeeded in getting the agrégation of mathematics (competitive national examination for teachers) in 2016 and specialized in optimization the following year.

I did a 4 months internship hosted by the LAAS-CNRS under the supervision of Jean-Bernard Lasserre and Edouard Pauwels about the computation of the empirical Christoffel function and its uses in outlier detection. The manuscript (in french). More info can be found on my LinkedIn page.

Benoît Tran

CERMICS, École Nationale des Ponts et Chaussées

6 et 8, av. Blaise Pascal

Cité Descartes - Champs-sur-Marne

77455 Marne-la-Vallée Cedex 2

France

E-mail: benoit.tran[at]enpc.fr