Nonlinear rescaling Lagrangians for nonconvex semidefinite programming

This paper focuses on the study of rescaling Lagrangians for solving nonconvex semidefinite programming problems. The rescaling nonlinear Lagrangians are generated by Löwner operators associated with convex real-valued functions. A set of conditions on the convex real-valued functions is proposed to...

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Bibliographic Details
Published in:Optimization Vol. 63; no. 6; pp. 899 - 920
Main Authors: Zhang, Liwei, Li, Yang, Wu, Jia
Format: Journal Article
Language:English
Published: Philadelphia Taylor & Francis 03.06.2014
Taylor & Francis LLC
Subjects:
Algorithms
augmented Lagrangian
Convergence
dual algorithm
Lagrange multiplier
Mathematical functions
Mathematical problems
Mathematical programming
nonlinear Lagrangian
Nonlinear programming
Nonlinearity
Operators
Optimization
Rescaling
Semidefinite programming
Studies
ISSN:0233-1934, 1029-4945
Online Access:Get full text
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Summary:This paper focuses on the study of rescaling Lagrangians for solving nonconvex semidefinite programming problems. The rescaling nonlinear Lagrangians are generated by Löwner operators associated with convex real-valued functions. A set of conditions on the convex real-valued functions is proposed to guarantee the convergence of nonlinear rescaling Lagrangian algorithms. These conditions are satisfied by well-known nonlinear Lagrangians appeared in the literature. The convergence theorem shows that, under the second-order sufficient conditions with sigma-term and the strict constraint nondegeneracy condition, the nonlinear rescaling Lagrange algorithm is locally convergent when the penalty parameter is less than a threshold and the error bound of solution is proportional to the penalty parameter. Compared to the analysis in the nonlinear rescaling Lagrangian method for nonlinear programming, we have to deal with the sigma term in the convergence analysis.
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ISSN:0233-1934
1029-4945
DOI:10.1080/02331934.2013.848861