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 ...

Munch, Arnaud Trélat, Emmanuel

It has been proved by Zuazua in the nineties that the internally controlled semilinear 1D wave equation ∂tty − ∂xxy + g(y) = f 1ω, with Dirichlet boundary conditions, is exactly controllable in H 1 0 (0, 1) ∩ L 2 (0, 1) with controls f ∈ L 2 ((0, 1) × (0, T)), for any T > 0 and any nonempty open subset ω of (0, 1), assuming that g ∈ C 1 (R) does no...

Tacchi, Matteo

Lasserre's moment-SOS hierarchy consists of approximating instances of the generalized moment problem (GMP) with moment relaxations and sums-of-squares (SOS) strenghtenings that boil down to convex semidefinite programming (SDP) problems. Due to the generality of the initial GMP, applications of this technology are countless, and one can cite among...

De Lara, Michel

Families are places of affection and cooperation, but also of conflict. In his famous paper Parent-Offspring Conflict, Robert L. Trivers builds upon W. D. Hamilton's concept of inclusive fitness to argue for genetic conflict in parent-offspring relationships, and to derive numerical predictions on the intensity of the conflict. We propose a mathema...

Ostrovskii, Dmitrii Bach, Francis

We demonstrate how self-concordance of the loss can be exploited to obtain asymptotically optimal rates for M-estimators in finite-sample regimes. We consider two classes of losses: (i) canonically self-concordant losses in the sense of Nesterov and Nemirovski (1994), i.e., with the third derivative bounded with the $3/2$ power of the second; (ii) ...

Ghattassi, Mohamed Laleg, Taous-Meriem Vivalda, Jean-Claude

This paper discusses the mathematical properties of a recently developed mathematical model of a direct contact membrane distillation system. The model consists of two-dimensional advection diffusion system coupled at the boundary. A semi-group framework is used to analyze the model. First, the infinitesimal generator operator and its properties ar...

Pérez Estigarribia, Pastor Bliman, Pierre-Alexandre Schaerer, Christian

Mosquitoes are vectors of viral diseases with epidemic potential in many regions of the world, and in absence of vaccines or therapies, their control is the main alternative. Chemical control through insecticides has been one of the conventional strategies, but induces insecticide resistance, which may affect other insects and cause ecological dama...

Henrot, A Lucardesi, I

In this paper we prove a new extremal property of the Reuleaux triangle: it maximizes the Cheeger constant among all bodies of (same) constant width. The proof relies on a fine analysis of the optimality conditions satisfied by an optimal Reuleaux polygon together with an explicit upper bound for the inradius of the optimal domain. As a possible pe...

Chaves Silva, Felipe W. Ervedoza, Sylvain Araujo De Souza, Diego

In this work, we push further the analysis of the problem of switching controls proposed in [31]. The problem consists in the following one: assuming that one can control a system using two or more actuators, does there exist a control strategy such that at all times, only one actuator is active? We answer positively to this question when the contr...

Mariette, Kévin Bideaux, Eric Bribiesca Argomedo, Federico Eberard, Damien Sesmat, Sylvie

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