Penalty technique for a min-max control problem
Using relaxed controls, optimality conditions are derived for a control problem where the cost ess sup G(x,u,t) is minimized. In reformulating the problem, we impose a unilateral constraint, which we deal with by a penalty method. Associated with the unilateral constraint, we obtain a multiplier \(\mu\) which is related to a measure dp. This measure is a positive Radon measure if G is continuous in all its arguments and is a finitely additive positive Radon measure if G is only measurable in the t-variable. We have indicated how the results of \textit{I. V. Girsanov} [see ''Lectures on mathematical theory of extremum problems'' (1972; Zbl 0234.49016)] follow from our results and how our results are related to those of \textit{K. Holmaker} [J. Optimization Theory Appl. 28, 391-410 (1979; Zbl 0387.49027)].
scientific article; zbMATH DE number 3951403