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|Title:||An inexact interior point method for L1-regularized sparse covariance selection||Authors:||Li, L.
|Keywords:||Inexact interior point method
Inexact search direction
Log-determinant semidefinite programming
Sparse inverse covariance selection
|Issue Date:||2010||Citation:||Li, L., Toh, K.-C. (2010). An inexact interior point method for L1-regularized sparse covariance selection. Mathematical Programming Computation 2 (3-4) : 291-315. ScholarBank@NUS Repository. https://doi.org/10.1007/s12532-010-0020-6||Abstract:||Sparse covariance selection problems can be formulated as logdeterminant (log-det) semidefinite programming (SDP) problems with large numbers of linear constraints. Standard primal-dual interior-point methods that are based on solving the Schur complement equation would encounter severe computational bottlenecks if they are applied to solve these SDPs. In this paper, we consider a customized inexact primal-dual path-following interior-point algorithm for solving large scale log-det SDP problems arising from sparse covariance selection problems. Our inexact algorithm solves the large and ill-conditioned linear system of equations in each iteration by a preconditioned iterative solver. By exploiting the structures in sparse covariance selection problems, we are able to design highly effective preconditioners to efficiently solve the large and ill-conditioned linear systems. Numerical experiments on both synthetic and real covariance selection problems show that our algorithm is highly efficient and outperforms other existing algorithms. © Springer and Mathematical Optimization Society 2010.||Source Title:||Mathematical Programming Computation||URI:||http://scholarbank.nus.edu.sg/handle/10635/102842||ISSN:||18672949||DOI:||10.1007/s12532-010-0020-6|
|Appears in Collections:||Staff Publications|
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