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Workshop MAC

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Friday 22 January 2021, LAAS-CNRS, Toulouse

## Scope

The workshop, organized by Didier Henrion, Mateusz Skomra and Sophie Tarbouriech, aims at introducing research topics at the crossroads between control, optimization, games and computer algebra.

## Date and venue

The workshop takes place on Friday 22 January 2021, in Salle du Conseil of LAAS-CNRS, 7 avenue du colonel Roche, 31400 Toulouse.

## Schedule

9:30-10:15 - Marianne Akian, INRIA and Ecole Polytechnique, Palaiseau
Tropical methods for solving stochastic control problems

Monotone discretizations of Hamilton-Jacobi-Bellman equations
lead to the dynamic programming equation
of a multi-stage stochastic optimization problem.
We develop several lower complexity numerical algorithms
for solving such equations by combining tropical or max-plus method,
numerical probabilistic approach,
and stochastic dual dynamic programming method.
This talk is based on joint works with Jean-Philippe Chancelier, Benoit Tran
and Eric Fodjo. See in particular arXiv:1709.09049, arXiv:1810.12870, arXiv:2010.10619.

10:30-11:15 - Nathanaël Fijalkow, LaBRI-CNRS, Univ. Bordeaux
Population protocols and probabilistic automata as linear dynamical systems

In this talk I will discuss two a priori different problems related to linear dynamical systems.
The first is a well-known model for distributed systems and the second an important notion in program verification.
I will show an unexpected connection between the two models, and present our current understanding for these problems, and conclude with a conjecture tying the two problems together.

11:30-12:15 - Simone Naldi, Univ. Limoges
On the complexity of semidefinite and hyperbolic programming

Semidefinite programming (SDP) can be seen as a special case of a more general conic optimization problem called hyperbolic programming (HP).
Although by construction HP is less explicit than SDP, the question whether there is a difference between these two classes is still an open problem
in the theory of hyperbolic polynomials (and it is conjectured that this is not the case). I will make an overview of some known results, mostly concerning
complexity questions around SDP and HP and concerning the problem of computing determinantal representations.