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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].
Reviewer: Reviewer (Berlin)
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
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