A Posteriori Error Estimates for Optimal Control Problems*

We present new a posteriori error estimates for approximate solutions of optimal control problems. Our approach is based on so-called functional a posteriori error estimates that were derived in the last decade for many elliptic and parabolic boundary value problems. They provide guaranteed two-sided bounds of approximation errors for any conforming approximation of a problem considered. In the paper, we consider optimal control problems with distributed control functions that enter right-hand sides of elliptic type state equations and apply functional a posteriori estimates to approximate solutions of state equations. This procedure leads to guaranteed two-sided estimates for the cost functional and also allows to obtain guaranteed a posteriori estimates for state and control functions.