Journal article
Interior-Point Algorithms for Semidefinite Programming Based on a Nonlinear Formulation
Computational optimization and applications, Vol.22(1), pp.49-79
04/01/2002
DOI: 10.1023/A:1014834318702
Abstract
Recently in Burer et al. (Mathematical Programming A, submitted), the authors of this paper introduced a nonlinear transformation to convert the positive definiteness constraint on an n x n matrix-valued function of a certain form into the positivity constraint on n scalar variables while keeping the number of variables unchanged. Based on this transformation, they proposed a first-order interior-point algorithm for solving a special class of linear semidefinite programs. In this paper, we extend this approach and apply the transformation to general linear semidefinite programs, producing nonlinear programs that have not only the n positivity constraints, but also n additional nonlinear inequality constraints. Despite this complication, the transformed problems still retain most of the desirable properties. We propose first-order and second-order interior-point algorithms for this type of nonlinear program and establish their global convergence. Computational results demonstrating the effectiveness of the first-order method are also presented. [PUBLICATION ABSTRACT]
Details
- Title: Subtitle
- Interior-Point Algorithms for Semidefinite Programming Based on a Nonlinear Formulation
- Creators
- Samuel Burer - University of IowaRenato D.C. MonteiroYin Zhang - Rice University
- Resource Type
- Journal article
- Publication Details
- Computational optimization and applications, Vol.22(1), pp.49-79
- Publisher
- Springer Nature B.V
- DOI
- 10.1023/A:1014834318702
- ISSN
- 0926-6003
- eISSN
- 1573-2894
- Language
- English
- Date published
- 04/01/2002
- Academic Unit
- Business Analytics
- Record Identifier
- 9984380519902771
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