A first-order block-decomposition method for solving two-easy-block structured semidefinite programs

Mathematical Programming Computation

Volumn 6, Issue 2, 2014, Pages 103-150

  Monteiro, Renato D C ^a   Ortiz, Camilo ^a   Svaiter, Benar F ^b  

^a Georgia Institute of Technology   (United States)

^b IMPA   (Brazil)

Author keywords

Block decomposition; Complexity; Conic optimization; Convex optimization; Extragradient; Proximal; Semidefinite programming

Indexed keywords

CONSTRAINED OPTIMIZATION; FREQUENCY ALLOCATION; LAGRANGE MULTIPLIERS;

BLOCK-DECOMPOSITION; COMPLEXITY; CONIC OPTIMIZATION; EXTRAGRADIENT; PROXIMAL; SEMI-DEFINITE PROGRAMMING;

CONVEX OPTIMIZATION;

EID: 84905855446     PISSN: 18672949     EISSN: 18672957     Source Type: Journal    
DOI: 10.1007/s12532-013-0062-7     Document Type: Article

References (22)

1. Burachik, R.S., Iusem, A.N., Svaiter, B.F.: Enlargement of monotone operators with applications to variational inequalities. Set Valued Anal. 5, 159-180 (1997). doi:10.1023/A:1008615624787
2. Burachik, R.S., Svaiter, B.F.: Maximal monotone operators, convex functions and a special family of enlargements. Set Valued Anal. 10, 297-316 (2002). doi:10.1023/A:1020639314056
3. Burer, S., Monteiro, R.D.C., Zhang,Y.:Acomputational study of a gradient-based log-barrier algorithm for a class of large-scale SDPs.Math. Program. 95, 359-379 (2003). doi:10.1007/s10107-002-0353-7
4. Chambolle, A., Pock, T.: A first-order primal-dual algorithm for convex problems with applications to imaging. J. Math. Imaging Vis. 40, 120-145 (2011). doi:10.1007/s10851-010-0251-1
5. Dolan, E.D., Moré, J.J.: Benchmarking optimization softwarewith performance profiles (2002). doi:10. 1007/s101070100263
6. Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Comput.Math.Appl. 2(1), 17-40 (1976). doi:10.1016/0898-1221(76)90003-1
7. Glowinski, R., Marrocco, A.: Sur l'approximation, par éléments finis d'ordre un, et la résolution, par penalisation-dualité, d'une classe de problèmes de dirichlet non linéaires. RAIRO Anal. Numér. 2, 41-76 (1975)
8. Lemaréchal, C.: Extensions diverses desméthodes de gradient et applications. Tech. rep., Thèse d'Etat, Université de Paris IX (1980)
9. Ma, S., Yin, W., Zhang, Y., Chakraborty, A.: An efficient algorithm for compressed mr imaging using total variation and wavelets. In: IEEE Conference on Computer Vision and Pattern Recognition, 2008. CVPR 2008, pp. 1-8 (2008). doi:10.1109/CVPR.2008.4587391
10. Malick, J., Povh, J., Rendl, F., Wiegele, A.: Regularization methods for semidefinite programming. SIAM J. Optim. 20(1), 336-356 (2009). doi:10.1137/070704575
11. Monteiro, R.C.D., Svaiter, B.F.: Iteration-complexity of block-decomposition algorithms and the alternating direction method of multipliers. SIAM J. Optim. 23(1), 475-507 (2013). doi:10.1137/110849468
12. Monteiro, R.D.C., Ortiz, C., Svaiter, B.F.: Implementation of a block-decomposition algorithm for solving large-scale conic semidefinite programming problems. Comput.Optim.Appl., pp. 1-25 (2013). doi:10.1007/s10589- 013-9590-3
13. Monteiro, R.D.C., Svaiter, B.F.: On the complexity of the hybrid proximal extragradient method for the iterates and the ergodic mean. SIAM J. Optim. 20(6), 2755-2787 (2010). doi:10.1137/090753127
14. Monteiro, R.D.C., Svaiter, B.F.: Complexity of variants of Tseng's modified F-B splitting and Korpelevich's methods for hemivariational inequalities with applications to saddle-point and convex optimization problems. SIAM J. Optim. 21(4), 1688-1720 (2011). doi:10.1137/100801652
15. Povh, J., Rendl, F.,Wiegele, A.: A boundary point method to solve semidefinite programs. Computing 78, 277-286 (2006). doi:10.1007/s00607-006- 0182-2
16. Rockafellar, R.T.: Convex Analysis. Princeton University Press, Princeton (1970)
17. Rockafellar,R.T.: On themaximal monotonicity of subdifferential mappings. Pac. J. Math. 33, 209-216 (1970)
18. Solodov, M.V., Svaiter, B.F.: A hybrid approximate extragradient-proximal point algorithm using the enlargement of a maximal monotone operator. Set Valued Anal. 7(4), 323-345 (1999
19. Svaiter, B.F.: A family of enlargements of maximal monotone operators. Set Valued Anal. 8, 311-328 (2000). doi:10.1023/A:1026555124541
20. Toh, K.C., Todd, M., Tütüncü, R.H.: Sdpt3-amatlab software package for semidefinite programming. Optim. Methods Softw. 11, 545-581 (1999)
21. Wen, Z., Goldfarb, D., Yin, W.: Alternating direction augmented lagrangian methods for semidefinite programming. Math. Program. Comput. 2, 203-230 (2010). doi:10.1007/s12532-010-0017-1
22. Zhao, X.Y., Sun, D., Toh, K.C.: A Newton-CG augmented lagrangian method for semidefinite programming. SIAM J. Optim. 20(4), 1737-1765 (2010). doi:10.1137/080718206