CHOMPACK is a library of algorithms for matrix computations with chordal sparsity patterns. It includes routines for Cholesky factorization and maximum determinant positive definite completion of chordal matrices, evaluation of the gradient, Hessian, and inverse Hessian of the logarithmic barrier function of a cone of positive definite matrices with chordal sparsity pattern, and evaluation of gradient, Hessian, and inverse Hessian of the conjugate barrier. The library provides efficient multifrontal implementations of the algorithms in the paper Covariance selection for non-chordal graphs via chordal embedding by J. Dahl, L. Vandenberghe, V. Roychowdhury (Optimization Methods and Software 23 (4), 501-520, 2008).

References in zbMATH (referenced in 11 articles )

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  1. Raghunathan, Arvind U.; Biegler, Lorenz T.: $LDL^T$ direction interior point method for semidefinite programming (2018)
  2. Li, Jinchao; Andersen, Martin S.; Vandenberghe, Lieven: Inexact proximal Newton methods for self-concordant functions (2017)
  3. Wang, Chengjing: On how to solve large-scale log-determinant optimization problems (2016)
  4. Andersen, Martin S.; Dahl, Joachim; Vandenberghe, Lieven: Logarithmic barriers for sparse matrix cones (2013)
  5. Carli, F.P.; Ferrante, A.; Pavon, M.; Picci, G.: An efficient algorithm for maximum entropy extension of block-circulant covariance matrices (2013)
  6. Huang, Hui; Haber, Eldad; Horesh, Lior: Optimal estimation of $\ell_1$-regularization prior from a regularized empirical Bayesian risk standpoint (2012)
  7. Yin, Jianxin; Li, Hongzhe: Model selection and estimation in the matrix normal graphical model (2012)
  8. Yun, Sangwoon; Tseng, Paul; Toh, Kim-Chuan: A block coordinate gradient descent method for regularized convex separable optimization and covariance selection (2011)
  9. Andersen, Martin S.; Dahl, Joachim; Vandenberghe, Lieven: Implementation of nonsymmetric interior-point methods for linear optimization over sparse matrix cones (2010)
  10. de Klerk, Etienne: Exploiting special structure in semidefinite programming: a survey of theory and applications (2010)
  11. Hesterberg, Tim; Choi, Nam Hee; Meier, Lukas; Fraley, Chris: Least angle and $\ell _1$ penalized regression: a review (2008)