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VOL. 33 | 1994 Monotone convergent methods for a variational inequality

Abstract

Penalty and path-following methods have been used for solving finitedimensional quadratic programmes. The intention here is to apply such techniques to an infinite-dimensional problem, namely a one-sided obstacle problem, and to develop a method for solving the problem in an infinite-dimensional setting. The numerical methods developed in the infinite-dimensional context, so the convergence rate of the discretisations are (in some sense) independent to the size of the finite-dimensional approximation. These methods are shown to be convergent in appropriate Banach spaces by means of a monotonicity result for the iterates of the associated Newton method. This montonicity carries over to finite-dimensional discretisations for a large class of methods. The overall numerical method developed is based on an exterior penalty fund;ion, and some num."erical results have been obtained.

Information

Published: 1 January 1994
First available in Project Euclid: 18 November 2014

zbMATH: 0853.49012
MathSciNet: MR1332514

Rights: Copyright © 1994, Centre for Mathematics and its Applications, Mathematical Sciences Institute, The Australian National University. This book is copyright. Apart from any fair dealing for the purpose of private study, research, criticism or review as permitted under the Copyright Act, no part may be reproduced by any process without permission. Inquiries should be made to the publisher.

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