Penalty method for the state equation for an elliptical optimal control problem

A. V. Lapin, D. G. Zalyalov

Chair of Mathematical Statistics, Kazan (Volga Region) Federal University, 18 Kremlyovskaya str., Kazan, 420008 Russia

Abstract: We solve an optimal control problem of a system governed by a linear elliptic equation with pointwise control constraints and non-local state constraints by finite difference method. A discrete optimal control problem is approximated by a minimization problem with penaltized state equation. We derive an error estimates. We also prove the rate of convergence of block Gauss–Zeidel iterative solution method for the penaltized problem. We present the results of the numerical experiments.

Keywords: constraint saddle point problem, optimal control, finite difference approximation, iterative methods.

UDC: 519.6

Received: 21.01.2014

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2015, 59:7, 31–43

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