![]() In: Reformulation: Nonsmooth, Piecewise Smooth, Semismooth and Smoothing Methods (Lausanne, 1997), volume 22 of Appl. 5(2), 159–180 (1997)īurachik, R.S., Sagastizábal, C.A., Svaiter, B.F.: □-enlargements of maximal monotone operators: theory and applications. 166(2), 391–413 (2015)īriceno-Arias, L., Davis, D.: Forward-backward-half forward algorithm with non self-adjoint linear operators for solving monotone inclusions preprint (2017)īurachik, R.S., Iusem, A.N., Svaiter, B.F.: Enlargement of monotone operators with applications to variational inequalities. Optimization 64(5), 1239–1261 (2015)īriceño Arias, L.M.: Forward-partial inverse-forward splitting for solving monotone inclusions. Springer, New York (2014)īriceño Arias, L.M.: Forward-Douglas-Rachford splitting and forward-partial inverse method for solving monotone inclusions. 36(8), 951–963 (2015)īoţ, R.I., Csetnek, E.R., Hendrich, C.: Recent developments on primal-dual splitting methods with applications to convex minimization. ![]() A), 251–279 (2015)īoţ, R.I., Csetnek, E.R.: A hybrid proximal-extragradient algorithm with inertial effects. With a foreword by Hédy Attouchīoţ, R.I., Csetnek, E.R., Heinrich, A., Hendrich, C.: On the convergence rate improvement of a primal-dual splitting algorithm for solving monotone inclusion problems. CMS Books in Mathematics/Ouvrages De Mathématiques De La SMC. ![]() 26(4), 2730–2743 (2016)īauschke, H.H., Combettes, P.L.: Convex analysis and monotone operator theory in hilbert spaces. Marques Alves, M., Monteiro, R.D.C., Svaiter, B.F.: Regularized HPE-type methods for solving monotone inclusions with improved pointwise iteration-complexity bounds. Finally, we perform simple numerical experiments to show the performance of the proposed methods when compared with other existing algorithms. We prove iteration complexity bounds for both algorithms in the pointwise (non-ergodic) as well as in the ergodic sense by showing that they admit two different iterations: one that can be embedded into the HPE method, for which the iteration complexity is known since the work of Monteiro and Svaiter, and another one which demands a separate analysis. Yao, in which an inexact DRS method is derived from a special instance of the hybrid proximal extragradient (HPE) method of Solodov and Svaiter, while the latter one combines the proposed inexact DRS method (used as an outer iteration) with a Tseng’s F-B splitting-type method (used as an inner iteration) for solving the corresponding subproblems. The former method (although based on a slightly different mechanism of iteration) is motivated by the recent work of J. ![]() ![]() In this paper, we propose and study the iteration complexity of an inexact Douglas-Rachford splitting (DRS) method and a Douglas-Rachford-Tseng’s forward-backward (F-B) splitting method for solving two-operator and four-operator monotone inclusions, respectively. ![]()
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