Suboptimal control of distributed parameter systems: Normality properties and dual subgradient method
type: Item
instance of: scholarly article
title: Suboptimal control of distributed parameter systems: Normality properties and dual subgradient method
zbMATH Open document ID: 0943.49019
author: M. I. Sumin
published in: Computational Mathematics and Mathematical Physics
publication date: 2000-06-19T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 49K20
Mathematics Subject Classification ID: 49J20
Mathematics Subject Classification ID: 90C52
Mathematics Subject Classification ID: 65K10
zbMATH DE Number: 1440452
zbMATH Keywords: optimal control
zbMATH Keywords: distributed parameter systems
zbMATH Keywords: suboptimal control
zbMATH Keywords: regularity
zbMATH Keywords: subgradient method
zbMATH Keywords: necessary optimality conditions
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1440452