Logarithmic barriers for sparse matrix cones

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.

References in corpus (2)

• Sparse Inverse Covariance Selection via Alternating Linearization Methods
• A Fully Sparse Implementation of a Primal-Dual Interior-Point Potential Reduction Method for Semidefinite Programming

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