Journal of Applied Mathematics
Volume 2012 (2012), Article ID 181629, 15 pages
Research Article

Generalized Quadratic Augmented Lagrangian Methods with Nonmonotone Penalty Parameters

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

Received 15 January 2012; Accepted 21 March 2012

Academic Editor: Ying U. Hu

Copyright © 2012 Xunzhi Zhu 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.


For nonconvex optimization problem with both equality and inequality constraints, we introduce a new augmented Lagrangian function and propose the corresponding multiplier algorithm. New iterative strategy on penalty parameter is presented. Different global convergence properties are established depending on whether the penalty parameter is bounded. Even if the iterative sequence { 𝑥 𝑘 } is divergent, we present a necessary and sufficient condition for the convergence of { 𝑓 ( 𝑥 𝑘 ) } to the optimal value. Finally, preliminary numerical experience is reported.