WIAS Preprint No. 1065, (2005)

Progressively refining penalized gradient projection method for semilinear parabolic optimal control problems



Authors

  • Chryssoverghi, Ion
  • Geiser, Juergen
  • Al-Hawasy, Jamil

2010 Mathematics Subject Classification

  • 93C83 74S05 35K20 47A05

2008 Physics and Astronomy Classification Scheme

  • 02.60.Cb 44.05.+e

Keywords

  • Optimal Control, Semilinear Parabolic Systems, Discretisation, Finite Element Method, Theta-Scheme, Discrete Penalized Gradient Projection Methods

Abstract

We consider an optimal control problem defined by semilinear parabolic partial differential equations, with control and state constraints, where the state constraints and cost functional involve also the state gradient. The problem is discretized by using a finite element method in space and an implicit -scheme in time for state approximation, while the controls are approximated by blockwise constant ones. We propose a discrete penalized gradient projection method, which is applied to the continuous problem and progressively refines the discretization during the iterations, thus reducing computing time and memory. We prove that strong accumulation points in of sequences generated by this method are admissible and weakly extremal for the continuous problem. Finally, numerical examples are given.

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