On Control‐Approximation Problems in Hilbert Spaces and Related Dual Problems: Subdifferentiability Properties and Estimates
Siegfried Dietze · ZAMM ‐ Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik · 1983
Abstract In this paper we consider abstract control‐approximation problems in Hilbert spaces, related dual problems and equivalent problems which arise from optimality conditions. We give the connections between these problems and study several properties of them, particularly properties concerning the subdifferentiability of the cost functionals. Furthermore, we derive estimates for the solutions and the optimal functional values. The results of this paper are above all useful for solving the control‐approximation problems, by the aid of the dual problems, directly or in connection with regularization methods.