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arXiv · 1203.2742

Logarithmic barriers for sparse matrix cones

Martin S. Andersen·Joachim Dahl·Lieven Vandenberghe
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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.

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Martin S. Andersen, Joachim Dahl, Lieven Vandenberghe. 2012-03-13. Logarithmic barriers for sparse matrix cones. https://doi.org/10.1080/10556788.2012.684353

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