In the first part of this paper the measure-theoretical approach to classical control problems, based on ideas of Young in variational calculus and developed by Rubio for control problems, was slightly extended by choosing a semi-infinite approach instead of a finite one. This results in a lower bound for the global minimum and an approximation for the optimal solution. It was still an open question, whether Rubio’s Approximation Theorem holds in the semi-infinite case and for more general boundary conditions. The second part of the paper deals with the discussion of the approximation properties and gives as an example the numerical treatment of a nice geometric extremal problem by Focke.
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Helmut Rudolph, The SILP-Relaxation Method in Optimal Control: General Boundary Conditions II. Z. Anal. Anwend. 11 (1992), no. 3, pp. 431–436DOI 10.4171/ZAA/592