Free Access
Volume 25, 2019
Article Number 57
Number of page(s) 14
Published online 25 October 2019
  1. M.M. Alves and M. Geremia, Iteration complexity of an inexact douglas-rachford method and of a Douglas-Rachford-Tseng’s F-B four-operator splitting method for solving monotone inclusions. Numer. Algorithms 82 (2019) 263–295 [Google Scholar]
  2. F.J.A. Artacho, J.M. Borwein and M.K. Tam, Recent results on Douglas-Rachford methods for combinatorial optimization problems. J. Optim. Theory Appl. 163 (2014) 1–30 [Google Scholar]
  3. T. Aspelmeier, C. Charitha and D.R. Luke, Local linear convergence of the ADMM/Douglas-Rachford algorithms without strong convexity and application to statistical imaging. SIAM J. Imaging Sci. 9 (2016) 842–868 [Google Scholar]
  4. J.M. Borwein and B. Sims, The Douglas-Rachford algorithm in the absence of convexity, in Fixed-point algorithms for inverse problems in science and engineering, Vol. 49 of Springer Optimization and its Applications. Springer, New York (2011) 93–109 [CrossRef] [Google Scholar]
  5. R.S. Burachik, A.N. Iusem, and B.F. Svaiter, Enlargement of monotone operators with applications to variational inequalities. Set-Valued Anal. 5 (1997) 159–180 [CrossRef] [Google Scholar]
  6. J. Douglas, Jr. and H.H. Rachford, Jr On the numerical solution of heat conduction problems in two and three space variables. Trans. Am. Math. Soc. 82 (1956) 421–439 [Google Scholar]
  7. J. Eckstein and D.P. Bertsekas, On the Douglas-Rachford splitting method and the proximal point algorithm for maximal monotone operators. Math. Program. 55 (1992) 293–318 [Google Scholar]
  8. J. Eckstein and B.F. Svaiter, A family of projective splitting methods for the sum of two maximal monotone operators. Math. Program. 111 (2008) 173–199 [Google Scholar]
  9. J. Eckstein and W. Yao, Relative-error approximate versions of Douglas–Rachford splitting and special cases of the ADMM. Math. Program. 170 (2017) 417–444 [Google Scholar]
  10. S. Fitzpatrick, Representing monotone operators by convex functions, in Workshop/Miniconference on Functional Analysis and Optimization. Vol. 20 of Proceedings of the Centre for Mathematics and its Analysis. Australian National University, Canberra (1988) 59–65 [Google Scholar]
  11. D. Gabay. Application of the method of multipliers to variational inequalities. Stud. Math. Appl. 15 (1983) 299–331 [CrossRef] [Google Scholar]
  12. R. Glowinski and S.J. Osher, Splitting Methods in Communication, Imaging, Science, and Engineering. Scientific Computation. Springer, Cham (2016) [CrossRef] [Google Scholar]
  13. R. Hesse and D.R. Luke, Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM J. Optim. 23 (2013) 2397–2419 [Google Scholar]
  14. R. Hesse, D.R. Luke and P. Neumann, Alternating projections and Douglas-Rachford for sparse affine feasibility. IEEE Trans. Signal Process. 62 (2014) 4868–4881 [Google Scholar]
  15. G. Li and T.K. Pong, Douglas-Rachford splitting for nonconvex optimization with application to nonconvex feasibility problems. Math. Program. 159 (2016) 371–401 [Google Scholar]
  16. J. Liang, J. Fadili, G. Peyré and R. Lukes, Activity identification and local linear convergence of Douglas-Rachford/ADMM under partial smoothness, in Scale space and variational methods in computer vision, Vol. 9087 of Lecture Notes in Computer Science. Springer, Cham (2015) 642–653 [Google Scholar]
  17. P.-L. Lions and B. Mercier, Splitting algorithms for the sum of two nonlinear operators. SIAM J. Numer. Anal. 16 (1979) 964–979 [Google Scholar]
  18. G.J. Minty, Monotone (nonlinear) operators in Hilbert space. Duke Math. J. 29 (1962) 341–346 [CrossRef] [MathSciNet] [Google Scholar]
  19. Z. Opial, Weak convergence of the sequence of successive approximations for nonexpansive mappings. Bull. Am. Math. Soc. 73 (1967) 591–597 [CrossRef] [MathSciNet] [Google Scholar]
  20. M.V. Solodov and B.F. Svaiter, A hybrid approximate extragradient-proximal point algorithm using the enlargement of a maximal monotone operator. Set-Valued Anal. 7 (1999) 323–345 [CrossRef] [Google Scholar]
  21. M.V. Solodov and B.F. Svaiter. A hybrid projection-proximal point algorithm. J. Convex Anal. 6 (1990) 59–70 [Google Scholar]
  22. M.V. Solodov and B.F. Svaiter, Error bounds for proximal point subproblems and associated inexact proximal point algorithms. Math. Program. 88 (2000) 371–389 [Google Scholar]
  23. M.V. Solodov and B.F. Svaiter, An inexact hybrid generalized proximal point algorithm and some new results on the theory of Bregman functions. Math. Oper. Res. 25 (2000) 214–230 [CrossRef] [Google Scholar]
  24. M.V. Solodov and B.F. Svaiter, A unified framework for some inexact proximal point algorithms. Numer. Funct. Anal. Optim. 22 (2001) 1013–1035 [Google Scholar]
  25. B.F. Svaiter, A family of enlargements of maximal monotone operators. Set-Valued Anal. 8 (2000) 311–328 [CrossRef] [Google Scholar]
  26. B.F. Svaiter, On weak convergence of the Douglas-Rachford method. SIAM J. Control Optim. 49 (2011) 280–287 [CrossRef] [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.