Mathematical Programming Computation

, Volume 2, Issue 3, pp 167–201

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


    • Electrical Engineering DepartmentUniversity of California
  • Joachim Dahl
    • MOSEK ApS
  • Lieven Vandenberghe
    • Electrical Engineering DepartmentUniversity of California
Open AccessFull Length Paper

DOI: 10.1007/s12532-010-0016-2

Cite this article as:
Andersen, M.S., Dahl, J. & Vandenberghe, L. Math. Prog. Comp. (2010) 2: 167. doi:10.1007/s12532-010-0016-2


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.

Mathematics Subject Classification (2000)

90-08 Mathematical Programming - computational methods90C06 Mathematical Programming - large-scale90C22 Mathematical Programming - semidefinite programing90C25 Mathematical Programming - convex programming90C51 Mathematical Programming - interior-point methods
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© The Author(s) 2010