Implementation of nonsymmetric interior-point methods for linear optimization over sparse matrix cones

We describe an implementation of nonsymmetric interior-point methods for linear cone programs defined by two types of matrix cones: the cone of positive semidefinite matrices with a given chordal sparsity pattern and its dual cone, the cone of chordal sparse matrices that have a positive semidefinit...

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Veröffentlicht in:Mathematical programming computation Jg. 2; H. 3-4; S. 167 - 201
Hauptverfasser: Andersen, Martin S., Dahl, Joachim, Vandenberghe, Lieven
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Berlin/Heidelberg Springer-Verlag 01.12.2010
Schlagworte:
Full Length Paper
Mathematics
Mathematics and Statistics
Mathematics of Computing
Operations Research/Decision Theory
Optimization
Theory of Computation
90C25 Mathematical Programming - convex programming
90-08 Mathematical Programming - computational methods
90C06 Mathematical Programming - large-scale
90C22 Mathematical Programming - semidefinite programing
90C51 Mathematical Programming - interior-point methods
ISSN:1867-2949, 1867-2957
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Zusammenfassung:We describe an implementation of nonsymmetric interior-point methods for linear cone programs defined by two types of matrix cones: the cone of positive semidefinite matrices with a given chordal sparsity pattern and its dual cone, the cone of chordal sparse matrices that have a positive semidefinite completion. The implementation takes advantage of fast recursive algorithms for evaluating the function values and derivatives of the logarithmic barrier functions for these cones. We present experimental results of two implementations, one of which is based on an augmented system approach, and a comparison with publicly available interior-point solvers for semidefinite programming.
ISSN:1867-2949
1867-2957
DOI:10.1007/s12532-010-0016-2