On Control‐Approximation Problems in Hilbert Spaces and Related Dual Problems: Subdifferentiability Properties and Estimates
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AbstractIn 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.
- TU Dresden Germany
Abstract differentiation theory, differentiation of set functions, Methods of successive quadratic programming type, Convex programming, Abstract approximation theory (approximation in normed linear spaces and other abstract spaces), Inner product spaces and their generalizations, Hilbert spaces, dual problems, abstract control-approximation problems, Existence theories for problems in abstract spaces, subdifferentiability of cost functionals, Optimality conditions for problems in abstract spaces, Duality theory (optimization)
Abstract differentiation theory, differentiation of set functions, Methods of successive quadratic programming type, Convex programming, Abstract approximation theory (approximation in normed linear spaces and other abstract spaces), Inner product spaces and their generalizations, Hilbert spaces, dual problems, abstract control-approximation problems, Existence theories for problems in abstract spaces, subdifferentiability of cost functionals, Optimality conditions for problems in abstract spaces, Duality theory (optimization)
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