Inertial viscosity forward–backward splitting algorithm for monotone inclusions and its application to image restoration problems

References

• F. Alvarez and H. Attouch, An inertial proximal method for maximal monotone operators via discretization of a nonlinear oscillator with damping. Set-Valued Anal. 9 (2001), pp. 3–11. doi: 10.1023/A:1011253113155
   Google Scholar
• J.B. Baillon and G. Haddad, Quelques proprietes des operateurs angle–bornes et cycliquement monotones, Isr. J. Math. 26 (1977), pp. 137–150. doi: 10.1007/BF03007664
   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
• P. Cholamjiak, A generalized forward–backward splitting method for solving quasi inclusion problems in Banach spaces, Numer Algor. 71 (2016), pp. 915–932. doi: 10.1007/s11075-015-0030-6
   Web of Science ®Google Scholar
• P. Cholamjiak, W. Cholamjiak and S. Suantai, A modified regularization method for finding zeros of monotone operators in Hilbert spaces, J. Ineq. Appl. 2015 (2015), p. 220. doi:10.1186/s13660-015-0739-8.
   Google Scholar
• W. Cholamjiak, P. Cholamjiak and S. Suantai, An inertial forward–backward splitting method for solving inclusion problems in Hilbert spaces, J. Fixed Point Theory Appl. 20 (2018), p. Art.42. 17. Available at https://doi.org/10.1007/s11784–018–0526–5. doi: 10.1007/s11784-018-0526-5
   Web of Science ®Google Scholar
• P. Cholamjiak and S. Suantai, Viscosity approximation methods for a nonexpansive semigroup in Banach spaces with gauge functions, J. Glob. Optim. 54 (2012), pp. 185–197. doi: 10.1007/s10898-011-9756-4
   Web of Science ®Google Scholar
• P.L. Combettes and R. Wajs, Signal recovery by proximal forward–backward splitting, Multiscale Model Simul. 4 (2005), pp. 1168–1200. doi: 10.1137/050626090
   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. doi: 10.1016/j.na.2010.02.010
   Web of Science ®Google Scholar
• E.T. Hale, W. Yin and Y. Zhang, A fixed–point continuation method for l1-regularized minimization with applications to compressed sensing, Tech. rep., CAAM TR07–07 2007.
   Google Scholar
• Y.Y. Huang and Y.D. Dong, New properties of forward–backward splitting and a practical proximal–descent algorithm, Appl Math Comput. 237 (2014), pp. 60–68.
   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. doi: 10.1137/0716071
   Web of Science ®Google Scholar
• G. López, V. Martín–Marquez, F. Wang and H.K. Xu, Forward–backward splitting methods for accretive operators in Banach spaces, Abstr. Appl. Anal., 2012.
   Google Scholar
• D. Lorenz and T. Pock, An inertial forward–backward algorithm for monotone inclusions, J. Math. Imaging Vis. 51 (2015), pp. 311–325. doi: 10.1007/s10851-014-0523-2
   Web of Science ®Google Scholar
• G. Marino and H.K. Xu, Convergence of generalized proximal point algorithm, Commun. Pure Appl. Anal. 3 (2004), pp. 791–808. doi: 10.3934/cpaa.2004.3.791
   Web of Science ®Google Scholar
• G. Marino and H.K. Xu, A general iterative method for nonexpansive mappings in Hilbert spaces, J. Math. Anal. Appl. 318 (2006), pp. 43–52. doi: 10.1016/j.jmaa.2005.05.028
   Web of Science ®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. doi: 10.1016/S0377-0427(02)00906-8
   Web of Science ®Google Scholar
• B.T. Polyak, Some methods of speeding up the convergence of iterative methods, Zh. Vychisl. Mat. Mat. Fiz. 4 (1964), pp. 1–17.
   Google Scholar
• B.T. Polyak, Introduction to Optimization, Optimization Software, Inc., Publications Division, New York, NY, USA, 1987.
   Google Scholar
• R.T. Rockafellar, On the maximality of subdifferential mappings, Pac. J. Math. 33 (1970), pp. 209–216. doi: 10.2140/pjm.1970.33.209
   Web of Science ®Google Scholar
• Y. Shehu and G. Cai, Strong convergence result of forward–backward splitting methods for accretive operators in banach spaces with applications, RACSAM., 2016.
   Google Scholar
• S. Sra, S. Nowozin and S.J. Wright, Optimization for Machine Learning, Cambridge, MIT Press, 2012.
   Google Scholar
• P. Sunthrayuth and P. Cholamjiak, Iterative methods for solving quasi–variational inclusion and fixed point problem in q-uniformly smooth Banach spaces, Numer. Algor. 78 (2018), pp. 1019–1044. doi: 10.1007/s11075-017-0411-0
   Web of Science ®Google Scholar
• R. Tibshirani, Regression shrinkage and selection via the lasso, J. Roy Stat Soc Ser B. 58 (1996), pp. 267–288.
   Google Scholar
• A.N. Tikhonov and V.Y. Arsenin, Solutions of Ill–posed problems, SIAM Rev. 21(2) (1979), pp. 266–267. doi: 10.1137/1021044
   Google Scholar
• P. Tseng, A modified forward–backward splitting method for maximal monotone mappings, SIAM J Control Optim. 38 (2000), pp. 431–446. doi: 10.1137/S0363012998338806
   Web of Science ®Google Scholar