Explicit algorithms to solve a class of state constrained parabolic optimal control problems

被引：8

作者：

Lapin, Alexander ^{[1
]}

Laitinen, Erkki ^{[2
]}

Lapin, Sergey ^{[3
]}

机构：

[1] Kazan Fed Univ, Kazan 420008, Russia

[2] Univ Oulu, Oulu 90014, Finland

[3] Washington State Univ, Pullman, WA 99164 USA

来源：

RUSSIAN JOURNAL OF NUMERICAL ANALYSIS AND MATHEMATICAL MODELLING | 2015年 / 30卷 / 06期

关键词：

Optimal control; finite difference method; constrained saddle point problem; iterative method; FINITE-ELEMENT APPROXIMATION; ELLIPTIC CONTROL-PROBLEMS; GRADIENT; REGULARIZATION; EQUATIONS;

D O I：

10.1515/rnam-2015-0032

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider an optimal control problem of a system governed by a linear parabolic equation with the following features: control is distributed, observation is either distributed or final, there are constraints on the state function and on its time derivative. Iterative solution methods are proposed and investigated for the finite difference approximations of these optimal control problems. Due to explicit in time approximation of the state equation and the appropriate choice of the preconditioners in the iterative methods, the implementation of all constructed methods is carried out by explicit formulae. Computational experiments confirm the theoretical results.

引用

页码：351 / 362

页数：12

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