On a fully adaptive SQP method for PDAE-constrained optimal control problems with control and state constraints.

*(English)*Zbl 1320.49015
Leugering, Günter (ed.) et al., Trends in PDE constrained optimization. Cham: Birkhäuser/Springer (ISBN 978-3-319-05082-9/hbk; 978-3-319-05083-6/ebook). ISNM. International Series of Numerical Mathematics 165, 85-108 (2014).

Summary: 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 [D. 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. Basel: Springer. 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.

For the entire collection see [Zbl 1306.49001].

For the entire collection see [Zbl 1306.49001].

Reviewer: Reviewer (Berlin)

##### MSC:

49M25 | Discrete approximations in optimal control |

49J20 | Existence theories for optimal control problems involving partial differential equations |

65C20 | Probabilistic models, generic numerical methods in probability and statistics |

65K10 | Numerical optimization and variational techniques |

65M60 | Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs |

90C46 | Optimality conditions and duality in mathematical programming |

90C55 | Methods of successive quadratic programming type |