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Logarithmic barriers for sparse matrix cones

Martin Andersen (martin.andersen***at***ucla.edu)
Joachim Dahl (dahl.joachim***at***gmail.com)
Lieven Vandenberghe (lieven.vandenberghe***at***ucla.edu)

Abstract: Algorithms are presented for evaluating gradients and Hessians of logarithmic barrier functions for two types of convex cones: the cone of positive semidefinite matrices with a given sparsity pattern, and its dual cone, the cone of sparse matrices with the same pattern that have a positive semidefinite completion. Efficient large-scale algorithms for evaluating these barriers and their derivatives are important in interior-point methods for nonsymmetric conic formulations of sparse semidefinite programs. The algorithms are based on the multifrontal method for sparse Cholesky factorization.

Keywords: Semidefinite programming, sparse matrix cones, multifrontal method

Category 1: Linear, Cone and Semidefinite Programming

Category 2: Linear, Cone and Semidefinite Programming (Semi-definite Programming )

Citation: Published in Optimization Methods and Software: http://www.tandfonline.com/doi/abs/10.1080/10556788.2012.684353

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Entry Submitted: 03/14/2012
Entry Accepted: 03/14/2012
Entry Last Modified: 06/13/2012

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