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

Mathematical Programming Computation volume 2, pages 167–201 (2010)Cite this article

Abstract

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.

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This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.

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Authors and Affiliations

  1. Electrical Engineering Department, University of California, Los Angeles, USA

    Martin S. Andersen & Lieven Vandenberghe

  2. MOSEK ApS, Fruebjergvej 3, 2100, Copenhagen Ø, Denmark

    Joachim Dahl

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  1. Martin S. Andersen
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  2. Joachim Dahl
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  3. Lieven Vandenberghe
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Correspondence to Martin S. Andersen.

Additional information

The authors’ (Andersen and Vandenberghe) research was supported in part by NSF grants ECS-0524663 and ECCS-0824003.

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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.

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Andersen, M.S., Dahl, J. & Vandenberghe, L. Implementation of nonsymmetric interior-point methods for linear optimization over sparse matrix cones. Math. Prog. Comp. 2, 167–201 (2010). https://doi.org/10.1007/s12532-010-0016-2

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  • DOI: https://doi.org/10.1007/s12532-010-0016-2

Mathematics Subject Classification (2000)

  • 90-08 Mathematical Programming - computational methods
  • 90C06 Mathematical Programming - large-scale
  • 90C22 Mathematical Programming - semidefinite programing
  • 90C25 Mathematical Programming - convex programming
  • 90C51 Mathematical Programming - interior-point methods