Numerical Method for a Dynamic Optimization Problem arising in the Modeling of a Population of Aerosol Particles Une Méthode Numérique pour un Problème d’Optimisation Dynamique lié à une Population de Particules

A model coupling differential equations and a sequence of constrained optimization problems is proposed to simulate the evolution of a population of particles at equilibrium interacting through a common medium. The first order optimality conditions of the optimization problems relaxed with barrier functions are coupled with the differential equations into a system of differential-algebraic equations that is discretized in time with an implicit first order scheme. The resulting system of nonlinear algebraic equations is solved at each time step with an interior-point/Newton method. The Newton system is block-structured and solved with Schur complement techniques, in order to take advantage of its sparsity. Application to the dynamics of a population of organic atmospheric aerosol particles is given to illustrate the evolution of particles of different sizes. To cite this article: A. Caboussat and A. Leonard, C. R. Acad. Sci., XX, (2008).