Constructive solution of a bilinear optimal control problem for a Schr'odinger equation

摘要

Often considered in numerical simulations related to the control of quantumsystems, the so-called monotonic schemes have not been so far much studied fromthe functional analysis point of view. Yet, these procedures provide anefficient constructive method for solving a certain class of optimal controlproblems. This paper aims both at extending the results already available aboutthese algorithms in the finite dimensional case (i.e., the time-discretizedcase) and at completing those of the continuous case. This paper starts withsome results about the regularity of a functional related to a wide class ofmodel in quantum chemistry. Those enable us to extend an inequality due to