H. Goldberg; F. Tröltzsch : On a SQP-multigrid technique for nonlinear parabolic boundary control problems

Author(s) :

H. Goldberg; F. Tröltzsch

Title :

On a SQP-multigrid technique for nonlinear parabolic boundary control problems

Electronic source :

[gzipped ps-file] 119 kB

Preprint series

Technische Universität Chemnitz-Zwickau, Fakultät für Mathematik (Germany). Preprint 97-11, 1997

Mathematics Subject Classification :

49M40 [ Methods of quadratic programming type ]

49M05 [ Methods of successive approximation based on necessary conditions ]

Abstract :

An optimal control problem governed by the heat equation with nonlinear boundary conditions is considered. The objective functional consists of a quadratic terminal part and a quadratic regularization term. It is known, that an SQP method converges quadratically to the optimal solution of the problem. To handle the quadratic optimal control subproblems with high precision, very large scale mathematical programming problems have to be treated. The constrained problem is reduced to an unconstrained one by a method due to Bertsekas. A multigrid approach developed by Hackbusch is applied to solve the unconstrained problems. Some numerical examples illustrate the behaviour of the method.

Keywords :

optimal control, semilinear parabolic equation, multigrig method, SQP method

Language :

english

Publication time :

4/1997