On the convergence of augmented Lagrangian methods for nonlinear semidefinite programming

In this paper, we present new convergence properties of the augmented Lagrangian method for nonlinear semidefinite programs (NSDP). Convergence to the approximately global solutions and optimal values of NSDP is first established for a basic augmented Lagrangian scheme under mild conditions, without...

Full description

Saved in:
Bibliographic Details
Published inJournal of global optimization Vol. 54; no. 3; pp. 599 - 618
Main Authors Luo, H. Z., Wu, H. X., Chen, G. T.
Format Journal Article
LanguageEnglish
Published Boston Springer US 01.11.2012
Springer Nature B.V
Subjects
Algorithms
Computer Science
Control theory
Eigenvalues
Lagrange multiplier
Mathematics
Mathematics and Statistics
Methods
Nonlinear equations
Nonlinear programming
Operations Research/Decision Theory
Optimization
Quadratic programming
Real Functions
Science
Semidefinite programming
Studies
Convergence to an
Modified augmented Lagrangian methods
Boundedness of multipliers
global solution
Nonlinear semidefinite program
Online AccessGet full text

Cover

More Information
Summary:In this paper, we present new convergence properties of the augmented Lagrangian method for nonlinear semidefinite programs (NSDP). Convergence to the approximately global solutions and optimal values of NSDP is first established for a basic augmented Lagrangian scheme under mild conditions, without requiring the boundedness condition of the multipliers. We then propose four modified augmented Lagrangian methods for NSDP based on different algorithmic strategies. We show that the same convergence of the proposed methods can be ensured under weaker conditions.
ISSN:0925-5001
1573-2916
DOI:10.1007/s10898-011-9779-x