Mathematical Problems in Engineering
Volume 2010 (2010), Article ID 324812, 13 pages
doi:10.1155/2010/324812
Research Article

Existence of Local Saddle Points for a New Augmented Lagrangian Function

Wenling Zhao, Jing Zhang, and Jinchuan Zhou

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

Received 27 March 2010; Revised 14 July 2010; Accepted 13 September 2010

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.

Abstract

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.