Vu, Trung-Hieu

This paper introduces and investigates a regularity condition in the asymptotic sense for the optimization problems whose objective functions are polynomial. We prove two sufficient conditions for the existence of solutions for polynomial optimization problems. Further, when the constraint sets are semi-algebraic, we show results on the stability o...

Chicoisne, Renaud

Cutting planes methods are of crucial importance to solve huge or nonconvex optimization problems. Minimizing a linear functional over general sets F may not be possible directly, however, optimizing on a wisely chosen relaxation R ⊇ F can be computationally tractable. Using the equivalence between optimization and separation, a popular approach co...

Ftouhi, Ilias Lamboley, Jimmy

We are interested in the study of Blaschke-Santaló diagrams describing the possible inequalities involving the first Dirichlet eigenvalue, the perimeter and the volume, for different classes of sets. We give a complete description of the diagram for the class of open sets in R d , basically showing that the isoperimetric and Faber-Krahn inequalitie...

Bompaire, Martin Désir, Antoine Heymann, Benjamin

Attribution-the mechanism that assigns conversion credits to individual marketing interactions-is one of the foremost digital marketing research topic. Indeed, attribution is used everywhere in online marketing whether for budget decisions or for the design of algorithmic bidders that the advertiser relies on to buy inventory. Still, an attribution...

Almeida, Luís Duprez, Michel Privat, Yannick Vauchelet, Nicolas

Mosquitoes are responsible for the transmission of many diseases such as dengue fever, zika or chigungunya. One way to control the spread of these diseases is to use the sterile insect technique (SIT), which consists in a massive release of sterilized male mosquitoes. This strategy aims at reducing the total population over time, and has the advant...

Asier Bárcena-Petisco, Jon

In this paper we consider the heat equation with Neumann, Robin and mixed boundary conditions (with coefficients on the boundary which depend on the space variable). The main results concern the behaviour of the cost of the null controllability with respect to the diffusion coefficient when the control acts in the interior. First, we prove that if ...

Duteil, Nastassia Piccoli, Benedetto

This paper focuses on a model for opinion dynamics, where the influence weights of agents evolve in time. We formulate a control problem of consensus type, in which the objective is to drive all agents to a final target point under suitable control constraints. Controllability is discussed for the corresponding problem with and without constraints ...

Assainova, Olga Rouot, Jérémy Sedgh-Gooya, Ehsan

In the context of data tokenization, we model a token as a vector of a finite dimensional metric space E and given a finite subset of E, called the token set, we address the problem of deciding whether a given token is in a small neighborhood of an other token. We derive conditions to characterize thenearest token of a given one and show that these...

Lissy, Pierre Moreau, Clément

We study the controllability of a coupled system of linear parabolic equations, with non-negativity constraint on the state. We establish two results of controllability to trajectories in large time: one for diagonal diffusion matrices with an "approximate" nonnegativity constraint, and a another stronger one, with "exact" nonnegativity constraint,...

Bernard, Olivier Lu, Liu-di Sainte Marie, Jacques Salomon, Julien

We consider a coupled physical-biological model describing growth of microalgae in a raceway pond cultivation process, accounting for hydrodynamics. Our approach combines a biological model (based on the Han model) and shallow water dynamics equations that model the fluid into the raceway pond. We present an optimization procedure dealing with the ...