A douglas-rachford type primal-dual method for solving inclusions with mixtures of composite and parallel-sum type monotone operators

SIAM Journal on Optimization

Volumn 23, Issue 4, 2013, Pages 2541-2565

  Boţ, Radu Ioan ^a   Hendrich, Christopher ^b  

^a UNIVERSITY OF VIENNA   (Austria)

^b CHEMNITZ UNIVERSITY OF TECHNOLOGY   (Germany)

Author keywords

Convex optimization; Douglas Rachford splitting; Fenchel duality; Monotone inclusion

Indexed keywords

BOUNDED LINEAR OPERATORS; DOUGLAS-RACHFORD SPLITTING; FENCHEL DUALITY; MONOTONE INCLUSIONS; NUMERICAL EXPERIMENTS; PRIMAL DUAL ALGORITHMS; PRIMAL-DUAL METHODS; SPLITTING ALGORITHMS;

ALGORITHMS; CONVEX OPTIMIZATION; MATHEMATICAL OPERATORS; MIXTURES;

ITERATIVE METHODS;

EID: 84892847325     PISSN: 10526234     EISSN: None     Source Type: Journal    
DOI: 10.1137/120901106     Document Type: Article

References (20)

1. H. H. Bauschke and P. L. Combettes, Convex Analysis and Monotone Operator Theory in Hilbert Spaces, CMS Books Math., Springer, New York, 2011.
2. A. Beck and M. Teboulle, A fast iterative shrinkage-tresholding algorithm for linear inverse problems, SIAM J. Imaging Sci., 2 (2009), pp. 183-202.
3. R. I. Boţ, Conjugate Duality in Convex Optimization, Lecture Notes in Econom. and Math. Systems 637, Springer, Berlin, 2010.
4. R. I. Boţ, E. R. Csetnek, and A. Heinrich, A primal-dual splitting algorithm for finding zeros of sums of maximally monotone operators, SIAM J. Optim., 23 (2013), pp. 2011-2036.
5. R. I. Boţ, S. M. Grad, and G. Wanka, Duality in Vector Optimization, Springer, Berlin, 2009.
6. R. I. Boţ and C. Hendrich, Convergence analysis for a primal-dual monotone + skew splitting algorithm with applications to total variation minimization, arXiv:1211.1706v1, 2012.
7. R. I. Boţ and C. Hendrich, An algorithm for solving monotone inclusions involving parallel sums of linearly composed maximally monotone operators, arXiv:1306.3191v1, 2013.
8. L. M. Briceño-Arias and P. L. Combettes, A monotone + skew splitting model for composite monotone inclusions in duality, SIAM J. Optim., 21 (2011), pp. 1230-1250.
9. A. Chambolle and T. Pock, A first-order primal-dual algorithm for convex problems with applications to imaging, J. Math. Imaging Vision, 40 (2011), pp. 120-145.
10. P. L. Combettes, Solving monotone inclusions via compositions of nonexpansive averaged operators, Optimization, 53 (2004), pp. 475-504.
11. P. L. Combettes, Iterative construction of the resolvent of a sum of maximal monotone operators, J. Convex Anal., 16 (2009), pp. 727-748.
12. P. L. Combettes and J.-C. Pesquet, Primal-dual splitting algorithm for solving inclusions with mixtures of composite, Lipschitzian, and parallel-sum type monotone operators, Set-Valued Var. Anal., 20 (2012), pp. 307-330.
13. L. Condat, A primal-dual splitting method for convex optimization involving Lipschitzian, proximable and linear composite terms, J. Optim. Theory Appl., 158 (2013), pp. 460-479.
14. B. S. Mordukhovich, N. M. Nam, and J. Salinas, Solving a generalized Heron problem by means of convex analysis, Amer. Math. Monthly, 119 (2012), pp. 87-99.
15. B. S. Mordukhovich, N. M. Nam, and J. Salinas, Applications of variational analysis to a generalized Heron problem, Appl. Anal., 91 (2012), pp. 1915-1942.
16. Y. Nesterov, Smooth minimization of non-smooth functions, Math. Program., 103 (2005), pp. 127-152.
17. 2), Soviet Math. Docl., 269 (1983), pp. 543-547.
18. P. Tseng, Applications of a splitting algorithm to decomposition in convex programming and variational inequalities, SIAM J. Optim., 29 (1991), pp. 119-138.
19. B. C. Vũ, A splitting algorithm for dual monotone inclusions involving cocoercive operators, Adv. Comp. Math., 38 (2013), pp. 667-681.
20. C. Zǎlinescu, Convex Analysis in General Vector Spaces, World Scientific, Singapore, 2002.