Tseng Type Methods for Inclusion and Fixed Point Problems with Applications

Abstract

An algorithm is introduced to find an answer to both inclusion problems and fixed point problems. This algorithm is a modification of Tseng type methods inspired by Mann’s type iteration and viscosity approximation methods. On certain conditions, the iteration obtained from the algorithm converges strongly. Moreover, applications to the convex feasibility problem and the signal recovery in compressed sensing are considered. Especially, some numerical experiments of the algorithm are demonstrated. These results are compared to those of the previous algorithm.

A parallel method for common variational inclusion and common fixed point problems with applications

“…The solution set of the problem (1.1) is represented as (F + G) −1 (0). The problem (1.1) can be interpreted as a model of numerous issues in different research fields, such as machine learning [8,21], signal processing [7,26] and image recovery [17,20]. Many splitting algorithms have been introduced and improved to find a solution to the variational inclusion problem (1.1), one of the most famous splitting algorithms is the forward-backward splitting algorithm, see in [12,18] for more details.…”

Modified Tseng’s Method with Inertial Viscosity Type for Solving Inclusion Problems and Its Application to Image Restoration Problems

“…In the algorithm (4), operators A and B are usually called the forward operator and the backward operator, respectively. For more details about forward-backward methods that have been constructed and considered to solve the inclusion problem (3), the reader is directed to [2,9,11,[24][25][26][27][28][29][30][31][32].…”

An inertial iterative scheme for solving variational inclusion with application to Nash-Cournot equilibrium and image restoration problems

“…Several variants of the forward-backward-forward method have been studied and a number of schemes have been presented to solve (1.1) (Refs. [1,6,19,23,24,27,32,33,49,52,53,55,58]). Inertial extrapolation techniques are introduced as a process of accelerating the convergence rate of an iterative scheme.…”