Optimal control methods are applied in various problems and can be efficient also for solving inverse problems, such as parameter identification and boundary control which arise in many important applications. For boundary optimal control methods one can identify conditions on an inaccessible part of the boundary by letting them play the role of a control variable function and by overimposing boundary conditions at another part of the boundary of the given domain.
The paper shows a mathematical formulation of the problem, the arising (regularized) Karush-Kuhn-Tucker (KKT) system and introduces a preconditioner for this system. The spectral analysis of the preconditioner and numerical tests with preconditioning are included.
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