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Abstract and Applied Analysis
Volume 2011 (2011), Article ID 902131, 14 pages
http://dx.doi.org/10.1155/2011/902131
Research Article

New Convergence Properties of the Primal Augmented Lagrangian Method

Department of Mathematics, School of Science, Shandong University of Technology, Zibo 255049, China

Received 23 August 2011; Revised 25 November 2011; Accepted 26 November 2011

Academic Editor: Simeon Reich

Copyright © 2011 Jinchuan Zhou 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

New convergence properties of the proximal augmented Lagrangian method is established for continuous nonconvex optimization problem with both equality and inequality constrains. In particular, the multiplier sequences are not required to be bounded. Different convergence results are discussed dependent on whether the iterative sequence generated by algorithm is convergent or divergent. Furthermore, under certain convexity assumption, we show that every accumulation point of is either a degenerate point or a KKT point of the primal problem. Numerical experiments are presented finally.