Inertial projection algorithms for convex feasibility problem

Abstract

The purpose of this paper is to apply inertial technique to string averaging projection method and block-iterative projection method in order to get two accelerated projection algorithms for solving convex feasibility problem. Compared with the existing accelerated methods for solving the problem, the inertial technique employs a parameter sequence and two previous iterations to get the next iteration and hence improves the flexibility of the algorithm. Theoretical asymptotic convergence results are presented under some suitable conditions. Numerical simulations illustrate that the new methods have better convergence than the general projection methods. The presented algorithms are inspired by the inertial proximal point algorithm for finding zeros of a maximal monotone operator.