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Journal of Applied Mathematics
Volume 2013 (2013), Article ID 976509, 9 pages
http://dx.doi.org/10.1155/2013/976509
Research Article

Global Convergence of a New Nonmonotone Filter Method for Equality Constrained Optimization

College of Mathematics and Computer Science, Hebei University, Baoding 071002, China

Received 6 December 2012; Accepted 5 March 2013

Academic Editor: Hadi Nasseri

Copyright © 2013 Ke Su et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

A new nonmonotone filter trust region method is introduced for solving optimization problems with equality constraints. This method directly uses the dominated area of the filter as an acceptability criterion for trial points and allows the dominated area decreasing nonmonotonically. Compared with the filter-type method, our method has more flexible criteria and can avoid Maratos effect in a certain degree. Under reasonable assumptions, we prove that the given algorithm is globally convergent to a first order stationary point for all possible choices of the starting point. Numerical tests are presented to show the effectiveness of the proposed algorithm.