Department of Mathematics, School of Science, Shandong University of Technology, Zibo 255049, China
Academic Editor: Joaquim J. Júdice
Copyright © 2010 Wenling Zhao 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.
We give a new class of augmented Lagrangian functions for nonlinear
programming problem with both equality and inequality constraints. The close relationship
between local saddle points of this new augmented Lagrangian and local optimal
solutions is discussed. In particular, we show that a local saddle point is a local optimal
solution and the converse is also true under rather mild conditions.