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A nonmonotonic trust region method for constrained optimization problems

Published online by Cambridge University Press:  17 February 2009

Jianzhong Zhang  and
Detong Zhu
Jianzhong Zhang
Affiliation:
Department of Mathematics, City University of Hong Kong, Hong Kong.
Detong Zhu
Affiliation:
Department of Mathematics, City University of Hong Kong, Hong Kong.
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Abstract

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In this paper we propose an easy-to-implement algorithm for solving general nonlinear optimization problems with nonlinear equality constraints. A nonmonotonic trust region strategy is suggested which does not require the merit function to reduce its value in every iteration. In order to deal with large problems, a reduced Hessian is used to replace a full Hessian matrix. To avoid solving quadratic trust region subproblems exactly which usually takes substantial computation, we only require an approximate solution which requires less computation. The calculation of correction steps, necessary from a theoretical view point to overcome the Maratos effect but which often brings in negative results in practice, is avoided in most cases by setting a criterion to judge its necessity. Global convergence and a local superlinear rate are then proved. This algorithm has a good performance.

Type
Research Article
Information
The ANZIAM Journal , Volume 40 , Issue 4 , April 1999 , pp. 542 - 567
Copyright
Copyright © Australian Mathematical Society 1999

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