A hybrid inertial and contraction proximal point algorithm for monotone variational inclusions

Convergence of Parameterized Variable Metric Three-Operator Splitting with Deviations for Solving Monotone Inclusions

“…Similar to (17) and (18), we obtain the following estimations of the third and the last terms of the right side in (21), respectively,…”

“…The inertial extrapolation technique and variable metric technique are two popular acceleration methods. The inertial extrapolation technique, or heavy ball method [17], has been widely studied in past decades; please see [18][19][20][21][22][23] and the references therein. The variable metric technique is a method to improve the convergence speed of the corresponding algorithm by changing the step size in each iteration.…”

Algorithms for Approximating Solutions of Split Variational Inclusion and Fixed-Point Problems

“…In particular, the variational inclusion theory is a natural development of the variational principle. A variety of approaches have been proposed for solving variational inclusion (2), see [19][20][21][22][23][24][25]. A valuable approach to solve (2) is the well-known forward-backward algorithm ( [26]) defined by…”