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 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 methods · 90C06 Mathematical Programming large-scale · 90C22 Mathematical Programming semidefinite programing · 90C25 Mathematical Programming convex programming · 90C51 Mathematical Programming interior-point methods The authors’ (Andersen and Vandenberghe) research was supported in part by NSF grants ECS-0524663 and ECCS-0824003. M. S. Andersen (B) · L. Vandenberghe Electrical Engineering Department, University of California, Los Angeles, USA e-mail: [email protected] L. Vandenberghe e-mail: [email protected] J. Dahl MOSEK ApS, Fruebjergvej 3, 2100 Copenhagen Ø, Denmark e-mail: [email protected]