Logarithmic barriers for sparse matrix cones

Martin Skovgaard Andersen, Joachim Dahl, Lieven Vandenberghe

Research output: Contribution to journalJournal articleResearchpeer-review


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.
Original languageEnglish
JournalOptimization Methods and Software
Pages (from-to)1-28
Publication statusPublished - 2012
Externally publishedYes

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