A NEWTON-PICARD APPROACH FOR EFFICIENT NUMERICAL SOLUTION OF TIME-PERIODIC PARABOLIC PDE CONSTRAINED OPTIMIZATION PROBLEMS

We investigate an iterative method for the solution of time-periodic parabolic PDE constrained optimization problems. It is an inexact Sequential Quadratic Programming (iSQP) method based on the Newton-Picard approach. We present and analyze a linear quadratic model problem and prove optimal mesh-independent convergence rates. Additionally, we propose a two-grid variant of the Newton-Picard method. Numerical results for the classical and the two-grid variants of the Newton-Picard iSQP method as a solver and as a preconditioner for GMRES are presented.

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