Suboptimal control of distributed parameter systems: Normality properties and dual subgradient method
By an example of an optimal control problem for a parabolic equation with weak solutions, elements of the suboptimal control theory of distributed parameter systems are considered. In terms of stationary and minimizing sequences, necessary and sufficient conditions for regularity and normality of the problem are established. The author presents a dual subgradient method for the numerical solution of this problem based on the maximization of the concave value function of the modified Lagrange functional. Then it is proved the convergence of this method and it is discussed the relation between this convergence and the ``degree'' to which the minimization of the initial problem, the constraints of this problem, and the necessary optimality conditions are all valid.
scientific article; zbMATH DE number 1440452