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

ABSTRACT In this research, we are interested about the monotone inclusion problems in the scope of the real Hilbert spaces by using an inertial forward–backward splitting algorithm. In addition, we have discussed the application of this algorithm.

[1]  R. Rockafellar,et al.  On the maximal monotonicity of subdifferential mappings. , 1970 .

[2]  R. Tibshirani.  Regression Shrinkage and Selection via the Lasso , 1996 .

[3]  Suthep Suantai,et al.  Viscosity approximation methods for a nonexpansive semigroup in Banach spaces with gauge functions , 2012, J. Glob. Optim..

[4]  A. Fischer,et al.  A family of operator splitting methods revisited , 2010 .

[5]  Prasit Cholamjiak,et al.  Iterative methods for solving quasi-variational inclusion and fixed point problem in q-uniformly smooth Banach spaces , 2017, Numerical Algorithms.

[6]  Patrick L. Combettes,et al.  Signal Recovery by Proximal Forward-Backward Splitting , 2005, Multiscale Model. Simul..

[7]  Giuseppe Marino,et al.  Convergence of generalized proximal point algorithms , 2004 .

[8]  P. Cholamjiak,et al.  An inertial forward–backward splitting method for solving inclusion problems in Hilbert spaces , 2018 .

[9]  O. Nelles,et al.  An Introduction to Optimization , 1996, IEEE Antennas and Propagation Magazine.

[10]  Dirk A. Lorenz,et al.  An Inertial Forward-Backward Algorithm for Monotone Inclusions , 2014, Journal of Mathematical Imaging and Vision.

[11]  Yuanyuan Huang,et al.  New properties of forward-backward splitting and a practical proximal-descent algorithm , 2014, Appl. Math. Comput..

[12]  J. Baillon,et al.  Quelques propriétés des opérateurs angle-bornés etn-cycliquement monotones , 1977 .

[13]  Hong-Kun Xu,et al.  Forward-Backward Splitting Methods for Accretive Operators in Banach Spaces , 2012 .

[14]  Prasit Cholamjiak,et al.  A generalized forward-backward splitting method for solving quasi inclusion problems in Banach spaces , 2015, Numerical Algorithms.

[15]  R. Willoughby.  Solutions of Ill-Posed Problems (A. N. Tikhonov and V. Y. Arsenin) , 1979 .

[16]  Giuseppe Marino,et al.  A general iterative method for nonexpansive mappings in Hilbert spaces , 2006 .

[17]  Heinz H. Bauschke,et al.  Convex Analysis and Monotone Operator Theory in Hilbert Spaces , 2011, CMS Books in Mathematics.

[18]  P. Lions,et al.  Splitting Algorithms for the Sum of Two Nonlinear Operators , 1979 .

[19]  A. N. Tikhonov,et al.  Solutions of ill-posed problems , 1977 .

[20]  H. Attouch,et al.  An Inertial Proximal Method for Maximal Monotone Operators via Discretization of a Nonlinear Oscillator with Damping , 2001 .

[21]  P. Cholamjiak,et al.  A modified regularization method for finding zeros of monotone operators in Hilbert spaces , 2015 .

[22]  Y. Shehu,et al.  Strong convergence result of forward–backward splitting methods for accretive operators in banach spaces with applications , 2018 .

[23]  Boris Polyak.  Some methods of speeding up the convergence of iteration methods , 1964 .

[24]  Paul Tseng,et al.  A Modified Forward-backward Splitting Method for Maximal Monotone Mappings 1 , 1998 .

[25]  Jean-Yves Audibert.  Optimization for Machine Learning , 1995 .

[26]  A. Moudafi,et al.  Convergence of a splitting inertial proximal method for monotone operators , 2003 .