Entropic proximal mappings with applications to nonlinear programming
Mathematics of Operations Research
Complementarity and nondegeneracy in semidefinite programming
Mathematical Programming: Series A and B
Determinant Maximization with Linear Matrix Inequality Constraints
SIAM Journal on Matrix Analysis and Applications
Computational Optimization and Applications
Smooth minimization of non-smooth functions
Mathematical Programming: Series A and B
Semismoothness of solutions to generalized equations and the Moreau-Yosida regularization
Mathematical Programming: Series A and B
Matrix Nearness Problems with Bregman Divergences
SIAM Journal on Matrix Analysis and Applications
The rate of convergence of the augmented Lagrangian method for nonlinear semidefinite programming
Mathematical Programming: Series A and B
The Journal of Machine Learning Research
First-Order Methods for Sparse Covariance Selection
SIAM Journal on Matrix Analysis and Applications
Constraint Nondegeneracy, Strong Regularity, and Nonsingularity in Semidefinite Programming
SIAM Journal on Optimization
Covariance selection for nonchordal graphs via chordal embedding
Optimization Methods & Software - Mathematical programming in data mining and machine learning
Smooth Optimization Approach for Sparse Covariance Selection
SIAM Journal on Optimization
Calibrating Least Squares Semidefinite Programming with Equality and Inequality Constraints
SIAM Journal on Matrix Analysis and Applications
Learning sparse Gaussian Markov networks using a greedy coordinate ascent approach
ECML PKDD'10 Proceedings of the 2010 European conference on Machine learning and knowledge discovery in databases: Part III
A Newton-CG Augmented Lagrangian Method for Semidefinite Programming
SIAM Journal on Optimization
Adaptive First-Order Methods for General Sparse Inverse Covariance Selection
SIAM Journal on Matrix Analysis and Applications
Alternating Direction Method for Covariance Selection Models
Journal of Scientific Computing
Robust Simulation of Global Warming Policies Using the DICE Model
Management Science
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We propose a Newton-CG primal proximal point algorithm (PPA) for solving large scale log-determinant optimization problems. Our algorithm employs the essential ideas of PPA, the Newton method, and the preconditioned CG solver. When applying the Newton method to solve the inner subproblem, we find that the log-determinant term plays the role of a smoothing term as in the traditional smoothing Newton technique. Focusing on the problem of maximum likelihood sparse estimation of a Gaussian graphical model, we demonstrate that our algorithm performs favorably compared to existing state-of-the-art algorithms and is much preferred when a high quality solution is required for problems with many equality constraints.