Properties of the Augmented Lagrangian in Nonlinear Semidefinite Optimization

We study the properties of the augmented Lagrangian function for nonlinear semidenite programming. It is shown that, under a set of sufcient conditions, the augmented Lagrangian algorithm is locally convergent when the penalty parameter is larger than a certain threshold. An error estimate of the so...

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Bibliographic Details
Published in:Journal of optimization theory and applications Vol. 129; no. 3; pp. 437 - 456
Main Authors: Sun, J., Zhang, L. W., Wu, Y.
Format: Journal Article
Language:English
Published: New York, NY Springer 01.06.2006
Springer Nature B.V
Subjects:
Algorithms
Applied sciences
Computer programming
Eigenvalues
Errors
Estimates
Exact sciences and technology
Lagrange multiplier
Nonlinearity
Operational research and scientific management
Operational research. Management science
Optimization
Programming
Quadratic programming
Studies
Thresholds
Semidefinite programming
Error estimation
convergence
Augmented Lagrangian
Semi definite programming
augmented Lagrangians
Non linear programming
Lagrangian function
ISSN:0022-3239, 1573-2878
Online Access:Get full text
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Summary:We study the properties of the augmented Lagrangian function for nonlinear semidenite programming. It is shown that, under a set of sufcient conditions, the augmented Lagrangian algorithm is locally convergent when the penalty parameter is larger than a certain threshold. An error estimate of the solution, depending on the penalty parameter, is also established. [PUBLICATION ABSTRACT]
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ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-006-9078-8