A block coordinate gradient descent method for regularized convex separable optimization and covariance selection

Mathematical Programming

Volumn 129, Issue 2, 2011, Pages 331-355

  Yun, Sangwoon ^a   Tseng, Paul ^b   Toh, Kim Chuan ^c  

^a Korea Institute for Advanced Study   (South Korea)

^b UNIVERSITY OF WASHINGTON   (United States)

^c NATIONAL UNIVERSITY OF SINGAPORE   (Singapore)

Author keywords

1 penalization; Block coordinate gradient descent; Complexity; Convex optimization; Covariance selection; Global convergence; Linear rate convergence; Maximum likelihood estimation

Indexed keywords

COMPLEXITY; COVARIANCE SELECTION; GLOBAL CONVERGENCE; GRADIENT DESCENT; LINEAR RATE;

APPROXIMATION THEORY; CONVERGENCE OF NUMERICAL METHODS; COVARIANCE MATRIX; IMAGE QUALITY; MAXIMUM LIKELIHOOD ESTIMATION; OPTIMIZATION;

CONVEX OPTIMIZATION;

EID: 81155131299     PISSN: 00255610     EISSN: 14364646     Source Type: Journal    
DOI: 10.1007/s10107-011-0471-1     Document Type: Article

References (20)

1. Borwein, J.M., Lewis, A.S.: Convex Analysis and Nonlinear Optimization: Theory and Examples. Springer, New York (2000)
2. Dahl, J., Vandenberghe, L., Roychowdhury, V.: Covariance selection for non-chordal graphs via chordal embedding. Optim. Methods Softw. 23, 501-520 (2008)
3. D'Aspremont, A., Banerjee, O., El Ghaoui, L.: First-order methods for sparse covariance selection. SIAM J. Matrix Anal. Appl. 30, 56-66 (2008)
4. Friedman, J., Hastie, T., Tibshirani, R.: Sparse inverse covariance estimation with the graphical lasso. Biostatistics 9, 432-441 (2008) (Pubitemid 351882084)
5. Goebel, R., Rockafellar, R.T.: Local strong convexity and local Lipschitz continuity of the gradients of convex functions. J. Convex Anal. 15, 263-270 (2008)
6. Horn, R., Johnson, C.: Matrix Analysis. Cambridge University Press, Cambridge (1999)
7. Lu, Z.: Smooth optimization approach for covariance selection. SIAM J. Optim. 19, 1807-1827 (2009)
8. Lu, Z.: Adaptive first-order methods for general sparse inverse covariance selection. SIAM J. Matrix Anal. Appl. 31, 2000-2016 (2010)
9. 2). Sov. Math. Doklady 27, 372-376 (1983)
10. Nesterov, Y.: Smooth minimization of nonsmooth functions. Math. Prog. 103, 127-152 (2005)
11. Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, New York (1999)
12. Rockafellar, R.T.: Convex Analysis. Princeton University Press, Princeton (1970)
13. Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Springer, New York (1998)
14. Saad, Y.: Iterative Methods for Sparse Linear Systems. PWS Publishing Company, Boston (1996)
15. Scheinberg, K., Rish, I.: Learning sparse Gaussian markov networks using a greedy coordinate ascent approach. In: Machine Learning and Knowledge Discovery in Databases. Lecture Notes in Computer Science, vol. 6323, pp. 196-212 (2010)
16. Tseng, P.: Convergence of block coordinate descent method for nondifferentiable minimization. J. Optim. Theory Appl. 109, 473-492 (2001)
17. Tseng, P.,Yun, S.:Acoordinate gradient descentmethod for nonsmooth separable minimization. Math. Prog. Ser. B 117, 387-423 (2009)
18. Wang, C., Sun, D., Toh, K.-C.: Solving log-determinant optimization problems by a Newton-CG primal proximal point algorithm. SIAM J. Optim. 20, 2994-3013 (2010)
19. Wong, F., Carter, C.K., Kohn, R.: Efficient estimation of covariance selection models. Biometrika 90, 809-830 (2003) (Pubitemid 39047121)
20. Yuan, X.: Alternating direction methods for sparse covariance selection. http://www.optimzationonline.org/DB-FILE/2009/09/2390.pdf