We found a match
Your institution may have rights to this item. Sign in to continue.
- Title
Saddle Points Theory of Two Classes of Augmented Lagrangians and Its Applications to Generalized Semi-infinite Programming.
- Authors
Changyu Wang; Jinchuan Zhou; Xiuhua Xu
- Abstract
In this paper, we develop the sufficient conditions for the existence of local and global saddle points of two classes of augmented Lagrangian functions for nonconvex optimization problem with both equality and inequality constraints, which improve the corresponding results in available papers. The main feature of our sufficient condition for the existence of global saddle points is that we do not need the uniqueness of the optimal solution. Furthermore, we show that the existence of global saddle points is a necessary and sufficient condition for the exact penalty representation in the framework of augmented Lagrangians. Based on these, we convert a class of generalized semi-infinite programming problems into standard semi-infinite programming problems via augmented Lagrangians. Some new first-order optimality conditions are also discussed.
- Subjects
LAGRANGIAN functions; NONCONVEX programming; METHOD of steepest descent (Numerical analysis); INFINITE matrices; MATHEMATICAL optimization; NUMERICAL analysis
- Publication
Applied Mathematics & Optimization, 2009, Vol 59, Issue 3, p413
- ISSN
0095-4616
- Publication type
Article
- DOI
10.1007/s00245-008-9060-y