A note on functional a posteriori estimates for elliptic optimal control problems
Provides rigorous error bounds for numerical solutions of constrained optimal control problems, benefiting computational scientists in PDE-constrained optimization.
This work derives new sharp, guaranteed, and fully computable lower bounds for the cost functional in elliptic optimal control problems with control constraints, enabling two-sided estimates and upper bounds for discretization errors. Numerical tests confirm efficiency.
In this work, new theoretical results on functional type a posteriori estimates for elliptic optimal control problems with control constraints are presented. More precisely, we derive new, sharp, guaranteed and fully computable lower bounds for the cost functional in addition to the already existing upper bounds. Using both, the lower and the upper bounds, we arrive at two-sided estimates for the cost functional. We prove that these bounds finally lead to sharp, guaranteed and fully computable upper estimates for the discretization error in the state and the control of the optimal control problem. First numerical tests are presented confirming the efficiency of the a posteriori estimates derived.