Ennaji, Hamza Igbida, Noureddine Nguyen, Van

We suggest a new approach to solve a class of degenerate Hamilton-Jacobi equations without any assumptions on the emptiness of the Aubry set. It is based on the characterization of the maximal subsolution by means of the Fenchel-Rockafellar duality. This approach enables us to use augmented Lagrangian methods as alternatives to the commonly used me...

KLOPFENSTEIN, QUENTIN Bertrand, Quentin Gramfort, Alexandre Salmon, Joseph Vaiter, Samuel

For composite nonsmooth optimization problems, Forward-Backward algorithm achieves model identification (e.g., support identification for the Lasso) after a finite number of iterations, provided the objective function is regular enough. Results concerning coordinate descent are scarcer and model identification has only been shown for specific estim...

Ennaji, Hamza Igbida, Noureddine Nguyen, Van

The aim of this note is to give a Beckmann-type problem as well as corresponding optimal mass transportation associated with a degenerate Hamilton-Jacobi equation H(x, ∇u) = 0, coupled with non-zero Dirichlet condition u = g on ∂Ω. In this article, Hamiltionian H is continuous in both arguments, coercive and convex in the second, but not enjoying a...

Lambert, Amélie

We consider the exact solution of problem $(QP)$ that consists in minimizing a quadratic function subject to quadratic constraints. Starting from the classical convex relaxation that uses the McCormick's envelopes, we introduce 12 inequalities that are derived from the ranges of the variables of $(QP)$. We prove that these general Triangle inequali...

Granzotto, Mathieu Postoyan, Romain Nešić, Dragan Buşoniu, Lucian Daafouz, Jamal

Value iteration (VI) is a ubiquitous algorithm for optimal control, planning, and reinforcement learning schemes. Under the right assumptions, VI is a vital tool to generate inputs with desirable properties for the controlled system, like optimality and Lyapunov stability. As VI usually requires an infinite number of iterations to solve general non...

Bernard, Olivier LU, Liu-di Salomon, Julien

This paper focuses on mixing strategies and designing shape of the bottom topographies to enhance the growth of the microalgae in raceway ponds. A physical-biological coupled model is used to describe the growth of the algae. A simple model of a mixing device such as a paddle wheel is also considered. The complete process model was then included in...

Duprez, Michel Lissy, Pierre

This work is devoted to the control of the Fokker-Planck equation, posed on a bounded domain of R^d (d>0). More precisely, the control is the drift force, localized on a small open subset. We prove that this system is locally controllable to regular nonzero trajectories. Moreover, under some conditions on the reference control, we explain how to re...

Letrouit, Cyril

It is well-known that observability (and, by duality, controllability) of the elliptic wave equation, i.e., with a Riemannian Laplacian, in time $T_0$ is almost equivalent to the Geometric Control Condition (GCC), which stipulates that any geodesic ray meets the control set within time $T_0$. We show that in the subelliptic setting, GCC is never ve...

Brivadis, Lucas Andrieu, Vincent Serres, Ulysse Gauthier, Jean-Paul

This paper deals with the observer design problem for time-varying linear infinite-dimensional systems. We address both the problem of online estimation of the state of the system from the output via an asymptotic observer, and the problem of offline estimation of the initial state via a Back and Forth Nudging (BFN) algorithm. In both contexts, we ...

Aronna, M Frédéric Bonnans, J Kröner, Axel

In this paper we consider an optimal control problem governed by a semilinear heat equation with bilinear control-state terms and subject to control and state constraints. The state constraints are of integral type, the integral being with respect to the space variable. The control is multidimensional. The cost functional is of a tracking type and ...