On a Fully Adaptive SQP Method for PDAE-Constrained Optimal Control Problems with Control and State Constraints

Abstract

We present an adaptive multilevel optimization approach which is suitable to solve complex real-world optimal control problems for time-dependent nonlinear partial differential algebraic equations with point-wise constraints on control and state. Relying on Moreau-Yosida regularization, the multilevel SQP method presented in Clever et al. (Generalized multilevel SQP-methods for PDAE-constrained optimization based on space-time adaptive PDAE solvers. In: Constrained optimization and optimal control for partial differential equations. Volume 160 of International series of numerical mathematics. Springer, Basel, pp 37–60, 2012) is extended to the state-constrained case. First-order convergence results are shown. The new multilevel SQP method is combined with the state-of-the-art software package KARDOS to allow the efficient resolution of different space and time scales in an adaptive manner. The numerical performance of the method is demonstrated and analyzed for a real-life three-dimensional radiative heat transfer problem modeling the cooling process in glass manufacturing and a two-dimensional thermistor problem modeling the heating process in steel hardening.