Three-operator reflected forward-backward splitting algorithm with double inertial effects

References

• F.J. Aragón-Artacho and D. Torregrosa-Belén, A direct proof of convergence of Davis–Yin splitting algorithm allowing larger stepsizes, Set-Valued Var. Anal. 30 (2022), pp. 1011–1029.
   Web of Science ®Google Scholar
• H. Attouch, J. Peypouquet, and P. Redont, Backward-forward algorithms for structured monotone inclusions in Hilbert spaces, J. Math. Anal. Appl. 457 (2018), pp. 1095–1117.
   Web of Science ®Google Scholar
• H.H. Bauschke and P.L. Combettes, Convex Analysis and Monotone Operator Theory in Hilbert Spaces, CMS Books in Mathematics, Springer, New York, 2011.
   Google Scholar
• A. Beck and M. Teboulle, A fast iterative shrinkage-thresholding algorithm for linear inverse problems, SIAM J. Imaging Sci. 2 (2009), pp. 183–202.
   Web of Science ®Google Scholar
• R.I. Boţ and E.R. Csetnek, An inertial forward-backward-forward primal-dual splitting algorithm for solving monotone inclusion problems, Numer. Algor. 71 (2016), pp. 519–540.
   Web of Science ®Google Scholar
• L.M. Briceño-Arias, Forward-Douglas-Rachford splitting and forward-partial inverse method for solving monotone inclusions, Optimization 64(5) (2015), pp. 1239–1261.
   Web of Science ®Google Scholar
• L.M. Briceño-Arias and D. Davis, Forward-backward-half forward algorithm for solving monotone inclusions, SIAM J. Optim. 28 (2018), pp. 2839–2871.
   Web of Science ®Google Scholar
• V. Cevher and B.C. Vũ, A reflected forward-backward splitting method for monotone inclusions involving Lipschitzian operators, Set-Valued Var. Anal. 29 (2021), pp. 163–174.
   Web of Science ®Google Scholar
• A. Chambolle and C. Dossal, On the convergence of the iterates of the fast iterative shrinkage/thresholding algorithm, J. Optim. Theory Appl. 166(3) (2015), pp. 968–982.
   Web of Science ®Google Scholar
• A. Chambolle and T. Pock, A first-order primal-dual algorithm for convex problems with applications to imaging, J. Math. Imaging Vis. 40(1) (2011), pp. 120–145.
   Web of Science ®Google Scholar
• P. Cholamjiak, D. Van Hieu, and Y.J. Cho, Relaxed forward–backward splitting methods for solving variational inclusions and applications, J. Sci. Comput. 88 (2021), pp. 85.
   Web of Science ®Google Scholar
• P.L. Combettes and J.C. Pesquet, Proximal splitting methods in signal processing, in Fixed Point Algorithms for Inverse Problems in Science and Engineering, Springer, New York, 2011, pp. 185–212.
   Google Scholar
• P.L. Combettes and V. Wajs, Signal recovery by proximal forward-backward splitting, SIAM Multiscale Model. Simul. 4 (2005), pp. 1168–1200.
   Web of Science ®Google Scholar
• L. Condat, A primal-dual splitting method for convex optimization involving Lipschitzian, proximable and linear composite terms, J. Optim. Theory Appl. 158(2) (2013), pp. 460–479.
   Web of Science ®Google Scholar
• E. Corman and X.M. Yuan, A generalized proximal point algorithm and its convergence rate, SIAM J. Optim. 24 (2014), pp. 1614–1638.
   Web of Science ®Google Scholar
• E.R. Csetnek, Y. Malitsky, and M.K. Tam, Shadow Douglas-Rachford splitting for monotone inclusions, Appl. Math. Optim. 80 (2019), pp. 665–678.
   Web of Science ®Google Scholar
• I. Daubechies, M. Defrise, and C. De Mol, An iterative thresholding algorithm for linear inverse problems with a sparsity constraint, Commun. Pure Appl. Math. 57 (2004), pp. 1413–1457.
   Web of Science ®Google Scholar
• D. Davis and W. Yin, A three-operator splitting scheme and its optimization applications, Set Valued Var. Anal. 25 (2017), pp. 829–858.
   Web of Science ®Google Scholar
• Y.D. Dong and A. Fischer, A family of operator splitting methods revisited, Nonlinear Anal. 72 (2010), pp. 4307–4315.
   Web of Science ®Google Scholar
• J. Douglas and H.H. Rachford, On the numerical solution of heat conduction problems in two or three space variables, Trans. Amer. Math. Soc. 82 (1956), pp. 421–439.
   Google Scholar
• J. Duchi and Y. Singer, Efficient online and batch learning using forward–backward splitting, J. Mach. Learn. Res. 10 (2009), pp. 2899–2934.
   Web of Science ®Google Scholar
• J. Fan, X. Qin, and B. Tan, Convergence of an inertial shadow Douglas-Rashford splitting algorithm for monotone inclusion, Numer. Funct. Anal. Optim. 42 (2021), pp. 1627–1644.
   Web of Science ®Google Scholar
• P. Latafat and P. Patrinos, Asymmetric forward-backward-adjoint splitting for solving monotone inclusions involving three operators, Comput. Optim. Appl. 68 (2017), pp. 57–93.
   Web of Science ®Google Scholar
• P.L. Lions and B. Mercier, Splitting algorithms for the sum of two nonlinear operators, SIAM J. Numer. Anal. 16 (1979), pp. 964–979.
   Web of Science ®Google Scholar
• D.A. Lorenz and T. Pock, An inertial forward-backward algorithm for monotone inclusions, J. Math. Imaging Vis. 51 (2015), pp. 311–325.
   Web of Science ®Google Scholar
• Y. Malitsky, Projected reflected gradient methods for monotone variational inequalities, SIAM J. Optim. 25 (2015), pp. 502–520.
   Web of Science ®Google Scholar
• Y. Malitsky and M.K. Tam, A forward-backward splitting method for monotone inclusions without cocoercivity, SIAM J. Optim. 30(2) (2020), pp. 1451–1472.
   Web of Science ®Google Scholar
• B. Martinet, Régularisation d'inéquations variationnelles par approximations successives, (French), Rev. Française Informat. Recherche Opérationnelle 4(1970), pp. 154–158. Sér. R-3.
   Google Scholar
• J.J. Moreau, Proximité et dualité dans un espace Hilbertien (French), Bull. Soc. Math. France 79 (1965), pp. 273–299.
   Google Scholar
• A. Moudafi and E. Elisabeth, An approximate inertial proximal method using the enlargement of a maximal monotone operator, Int. J. Pure Appl. Math. 5 (2003), pp. 283–299.
   Google Scholar
• A. Moudafi and M. Oliny, Convergence of a splitting inertial proximal method for monotone operators, J. Comput. Appl. Math. 155 (2003), pp. 447–454.
   Web of Science ®Google Scholar
• Y. Nesterov, A method of solving a convex programming problem with convergence rate O( 1/k2), Soviet Math. Doklady 27 (1983), pp. 372–376.
   Google Scholar
• B.T. Polyak, Some methods of speeding up the convergence of iteration methods, U.S.S.R. Comput. Math. Math. Phys. 4(5) (1964), pp. 1–17.
   Google Scholar
• H. Raguet, J. Fadili, and G. Peyre, A generalized forward-backward splitting, SIAM J. Imaging Sci. 6 (2013), pp. 1199–1226.
   Web of Science ®Google Scholar
• J. Rieger and M.K. Tam, Backward-forward-reflected-backward splitting for three operator monotone inclusions, Appl. Math. Comput. 381 (2020), pp. 125248. 10 pp.
   Web of Science ®Google Scholar
• R.T. Rockafellar, Monotone operators and the proximal point algorithm, SIAM J. Control Optim. 14 (1976), pp. 877–898.
   Web of Science ®Google Scholar
• E.K. Ryu, Uniqueness of DRS as the 2 operator resolvent-splitting and impossibility of 3 operator resolvent-splitting, Math. Program. 182 (2020), pp. 233–273.
   Web of Science ®Google Scholar
• E.K. Ryu and S. Boyd, A primer on monotone operator methods, Appl. Comput. Math. 15 (2016), pp. 3–43.
   Web of Science ®Google Scholar
• E.K. Ryu and B.C. Vũ, Finding the forward-Douglas–Rachford-forward method, J. Optim. Theory Appl. 184 (2020), pp. 858–876.
   Web of Science ®Google Scholar
• P. Tseng, A modified forward-backward splitting method for maximal monotone mappings, SIAM J. Control Optim. 38(2) (2000), pp. 431–446.
   Web of Science ®Google Scholar
• B.C. Vũ, A splitting algorithm for dual monotone inclusions involving cocoercive operators, Adv. Comput. Math. 38(3) (2013), pp. 667–681.
   Web of Science ®Google Scholar
• Z. Wu and M. Li, General inertial proximal gradient method for a class of nonconvex nonsmooth optimization problems, Comp. Optim. Appl. 73 (2019), pp. 129–158.
   Web of Science ®Google Scholar
• H. Yu, C. Zong, and Y. Tang, An outer reflected forward-backward splitting algorithm for solving monotone inclusions, arXiv:2009.12493v1; 2020.
   Google Scholar
• C. Zong, Y. Tang, and Y.J. Cho, Convergence analysis of an inexact three-operator splitting algorithm, Symmetry 10 (2018), pp. 563.
   Google Scholar
• C. Zong, Y. Tang, and G. Zhang, An accelerated forward-backward-half forward splitting algorithm for monotone inclusion with applications to image restoration, Optimization. doi:10.1080/02331934.2022.2107926
   Web of Science ®Google Scholar
• C.X. Zong, Y.C. Tang, and G.F. Zhang, An inertial semi-forward-reflected-backward splitting and its application, Acta. Math. Sin. English Ser. 38 (2022), pp. 443–464.
   Web of Science ®Google Scholar