Nouvelles Methodes en Contrôle Impulsionnel

This article develops a general methodology for solving optimal impulse control problems. The basic tool is the concept of quasi-variational inequalities. These inequalities play for impulse control a part similar to Hamilton-Jacobi-Bellman equations for continuous control theory. The concept of quasi variational inequality generalizes the concept of variational inequality. One gives a theorem of existence of a solution of a quasi variational inequality and one shows that it is possible to deduce from it an optimal solution for a problem of impulse control. © 1975 Springer-Verlag New York Inc.