Progressively Refining Discrete Gradient Projection Method for Semilinear Parabolic Optimal Control Problems

  • Ion Chryssoverghi
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3401)


We consider an optimal control problem defined by semilinear parabolic partial differential equations, with convex control constraints. Since this problem may have no classical solutions, we also formulate it in relaxed form. The classical problem is then discretized by using a finite element method in space and a theta-scheme in time, where the controls are approximated by blockwise constant classical ones. We then propose a discrete, progressively refining, gradient projection method for solving the classical, or the relaxed, problem. We prove that strong accumulation points (if they exist) of sequences generated by this method satisfy the weak optimality conditions for the continuous classical problem, and that relaxed accumulation points (which always exist) satisfy the weak optimality conditions for the continuous relaxed problem. Finally, numerical examples are given.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Ion Chryssoverghi
    • 1
  1. 1.Department of MathematicsNational Technical University of AthensAthensGreece

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