Logarithmic barriers for sparse matrix cones
Optimization and Control
2012-06-15 v1 Numerical Analysis
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.
Cite
@article{arxiv.1203.2742,
title = {Logarithmic barriers for sparse matrix cones},
author = {Martin S. Andersen and Joachim Dahl and Lieven Vandenberghe},
journal= {arXiv preprint arXiv:1203.2742},
year = {2012}
}