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In this paper, we propose a randomized intertial block-coordinate primaldual fixed point algorithm to solve a wide array of monotone inclusion problems base on the modification of the heavy ball method of Nesterov.
Polyak, B.T.: Some methods of speeding up the convergence of iteration methods. U.S.S.R. Comput. Math. Math. Phys. 4(5), 1-17 (1964)
1964
Earlier work this paper cites.
E. Raik, Fejér type methods in Hilbert space, Eesti NSV Tead. Akad. Toimetised Füü.-Mat.s, vol. 16, pp. 286-293, 1967
1967
Earlier work this paper cites.
Yu. M. Ermole’v, On the method of generalized stochastic gradients and quasi-Fej¡äer sequences, Cybernetics, vol. 5, pp. 208-220, 1969
1969
Earlier work this paper cites.
J. M. Ortega and W. C. Rheinboldt, Iterative Solution of Nonlinear Equations in Several Variables, Academic Press, New York, 1970
1970
Earlier work this paper cites.
Yu. M. Ermol’ev, On convergence of random Fejér sequences, Cybernetics, vol. 7, pp. 655-656, 1971
1971
Earlier work this paper cites.
A. Auslender, Méthodes numériques pour la décomposition et la minimisation de fonctions non différentiables, Numer. Math., vol. 18, pp. 213-223, 1971/72
1971
Earlier work this paper cites.
J. Céa, Optimisation: Théorie et Algorithmes, Dunod, Paris, 1971
1971
Earlier work this paper cites.
Yu. M. Ermol’ev and A. D. Tuniev, Random Fejér and quasi-Fejér sequences, Theory of Optimal Solutions¨C Akademiya Nauk Ukrainskol̆ SSR Kiev, vol. 2, pp. 76-83, 1968; translated in: American Mathematical Society Selected Translations in Mathematical Statistics and Probability, vol. 13, pp. 143-148, 1973
1973
Earlier work this paper cites.
1983
Earlier work this paper cites.
Eckstein, J., Bertsekas, D.P.: On the Douglas¨CRachford splitting method and the proximal point algorithm for maximal monotone operators. Math. Program. 55, 293-318 (1992)
1992
Earlier work this paper cites.
H. H. Bauschke and P. L. Combettes, A weak-to-strong convergence principle for Fejér-monotone methods in Hilbert spaces, Math. Oper. Res., vol. 26, pp. 248-264, 2001
2001
Earlier work this paper cites.
N.Ogura, and I. Yamada, Non-strictly convex minimization over the fixed point set of an asymptotically shrinking nonexpansive mapping. Numer. Funct. Anal. Optim., vol. 23 (1-2), pp. 113-137, 2002
2002
Earlier work this paper cites.
Nesterov, Y.: Introductory lectures on convex optimization: a basic course. In: Applied Optimization, vol. 87. Kluwer Academic Publishers, Boston, MA (2004)
2004
Earlier work this paper cites.
P. L. Combettes, Fejér monotonicity in convex optimization, in: Encyclopedia of Optimization, 2nd ed. (C. A. Floudas and P. M. Pardalos, eds.), pp. 1016-1024. Springer, New York, 2009
2009
Earlier work this paper cites.
I. I. Eremin and L. D. Popov, Fejér processes in theory and practice: Recent results, Russian Math. (Iz. VUZ), vol. 53, pp. 36-55, 2009
2009
Cited alongside, same era.
E. Esser, X. Zhang, and T. Chan. A general framework for a class of first order primal-dual algorithms for convex optimization in imaging science. SIAM J. Imaging Sci., 3(4):1015-1046, 2010
2010
Cited alongside, same era.
A. Chambolle and T. Pock. A first-order primal-dual algorithm for convex problems with applications to imaging. J. Math. Imaging Vision, 40(1):120-145, 2011
2011
Cited alongside, same era.
I. Loris and C. Verhoeven. On a generalization of the iterative soft-thresholding algorithm for the case of non-separable penalty. Inverse Problems, 27(12):125007, 2011
2011
Cited alongside, same era.
H. H. Bauschke and P. L. Combettes, Convex Analysis and Monotone Operator Theory in Hilbert Spaces. Springer, New York, 2011
P. L. Combettes. Systems of structured monotone inclusions: duality, algorithms, and applications. SIAM J. Optim., 23(4):2420-2447, Dec. 2013
2013
Later among the works it cites.
L. Condat. A primal-dual splitting method for convex optimization involving Lipschitzian, proximable and linear composite terms. J. Optim. Theory Appl., 158(2):460-479, Aug. 2013
2013
Later among the works it cites.
B. C. Vũ. A splitting algorithm for dual monotone inclusions involving cocoercive operators. Adv. Comput. Math., 38(3):667-681, Apr. 2013
2013
Later among the works it cites.
P. Chen, J. Huang, and X. Zhang. A primal-dual fixed point algorithm for convex separable minimization with applications to image restoration. Inverse Problems, 29(2):025011, 2013
2013
Later among the works it cites.
C. Couprie, L. Grady, L. Najman, J.-C. Pesquet, and H. Talbot. Dual constrained TV-based regularization on graphs. SIAM J. Imaging Sci., 6:1246-1273, 2013
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2011
Cited alongside, same era.
L. M. Briceño-Arias, A Douglas-Rachford splitting method for solving equilibrium problems. Nonlinear Anal., 75(16):6053-6059, Nov. 2012
2012
Cited alongside, same era.
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(2):307-330, June 2012
2012
Cited alongside, same era.
J.C. Pesquet and N. Pustelnik, A parallel inertial proximal optimization method. Pac. J. Optim., 8(2):273-305, Apr. 2012
2012
Cited alongside, same era.
B. He and X. Yuan. Convergence analysis of primal-dual algorithms for a saddle-point problem: from contraction perspective. SIAM J. Imaging Sci., 5(1):119-149, 2012
2012
Cited alongside, same era.
A. Jezierska, E. Chouzenoux, J.-C. Pesquet, and H. Talbot. A primal-dual proximal splitting approach for restoring data corrupted with Poisson-Gaussian noise. In Proc. Int. Conf. Acoust., Speech Signal Process., pages 1085-1088, Kyoto, Japan, 25-30 Mar. 2012
2012
Cited alongside, same era.
A. Repetti, E. Chouzenoux, and J.-C. Pesquet. A penalized weighted least squares approach for restoring data corrupted with signal-dependent noise. In Proc. Eur. Sig. and Image Proc. Conference, pages 1553-1557, Bucharest, Romania, 27-31 Aug. 2012
2012
Cited alongside, same era.
R. I. Boţ, and C. Hendrich, A Douglas-Rachford type primal-dual method for solving inclusions with mixtures of composite and parallel-sum type monotone operators. SIAM J. Optim., 23(4):2541-2565, Dec. 2013
2013
Cited alongside, same era.
2013
Later among the works it cites.
S. Harizanov, J.-C. Pesquet, and G. Steidl. Epigraphical projection for solving least squares Anscombe transformed constrained optimization problems. In A. Kuijper et al., editor, 4th International Conference on Scale-Space and Variational Methods in Computer Vision, volume 7893 of Lecture Notes in Computer Science, pages 125-136, Schloss Seggau, Leibnitz, Austria, 2-6 June 2013. Springer-Verlag, Berlin
2013
Later among the works it cites.
T. Teuber, G. Steidl, and R.-H. Chan. Minimization and parameter estimation for seminorm regularization models with I I -divergence constraints. Inverse Problems, 29:035007, Mar. 2013
2013
Later among the works it cites.
P. L. Combettes and J. C. Pesquet, Stochastic Quasi-Fejér Block-Coordinate Fixed Point Iterations with Random Sweeping, 2014, http://www.optimization-online.org/DB HTML/2014/04/4333.html
2014
Later among the works it cites.
2014
Later among the works it cites.
D. A. Lorenz and¡¤ T. Pock. An Inertial Forward-Backward Algorithm for Monotone Inclusions. J Math Imaging Vis DOI 10.1007/s10851-014-0523-2, 2014
2014
Later among the works it cites.
S. R. Becker and P. L. Combettes. An algorithm for splitting parallel sums of linearly composed monotone operators, with applications to signal recovery. J. Nonlinear Convex Anal., 15(1):137-159, Jan. 2014
2014
Later among the works it cites.
N. Pustelnik, P. Borgnat, and P. Flandrin. Empirical Mode Decomposition revisited by multicomponent nonsmooth convex optimization. Signal Process., 102:313-331, Sept. 2014
2014
Later among the works it cites.
R. I. Boţ, E. R. Csetnek and C. Hendrich, Inertial Douglas-Rachford splitting for monotone inclusion problems, Appl. Math. Comput., vol. 256, pp. 472-487, 2015
2015
Later among the works it cites.