A note on numerical solution of dynamical optimization problems (Q2266571)

This note is concerned with optimal control problems governed by evolution partial differential equations in abstract Hilbert spaces. The state and the control are subject to general convex constraints. The problem is approximated first by the penalty function technique of \textit{A. V. Balakrishnan} [SIAM J. Control 6, 149-173 (1968; Zbl 0174.408)]. Next every penalized problem is treated by a technique of approximation (in Banach spaces) due to \textit{S. De Julio} [ibid. 8, 135-147 (1970; Zbl 0223.49036)]. Convergence theorems are formulated. The results of this note extend those of Julio to the case of more general constraints.