Convergence of the SQP method for quasilinear parabolic optimal control problems

Abstract

AbstractBased on the theoretical framework recently proposed by Bonifacius and Neitzel (Math Control Relat Fields 8(1):1–34, 2018. 10.3934/mcrf.2018001) we discuss the sequential quadratic programming (SQP) method for the numerical solution of an optimal control problem governed by a quasilinear parabolic partial differential equation. Following well-known techniques, convergence of the method in appropriate function spaces is proven under some common technical restrictions. Particular attention is payed to how the second order sufficient conditions for the optimal control problem and the resulting $$L^2$$ L 2 -local quadratic growth condition influence the notion of “locality” in the SQP method. Further, a new regularity result for the adjoint state, which is required during the convergence analysis, is proven. Numerical examples illustrate the theoretical results.