Modified Projection Method with Inertial Technique and Hybrid Stepsize for the Split Feasibility Problem

A Perturbed Projection Algorithm with Inertial Technique for Split Feasibility Problem

This paper deals with the split feasibility problem that requires to find a point closest to a closed convex set in one space such that its image under a linear transformation will be closest to another closed convex set in the image space. By combining perturbed strategy with inertial technique, we construct an inertial perturbed projection algorithm for solving the split feasibility problem. ...

Modified Halfspace-Relaxation Projection Methods for Solving the Split Feasibility Problem

A Modified Algorithm for Solving the Split Feasibility Problem

In this paper a modified algorithm for solving the split feasibility problem (SFP) is presented. This algorithm uses the generalized Armijo line search in computing predictor step size and gives a correction step rule in the iterative process, which makes an accelerated convergence to the solution of SFP. Meanwhile, it needs not to compute the matrix inverses and the large eigenvalue of the mat...

A Splitting-relaxed Projection Method for Solving the Split Feasibility Problem

The split feasibility problem (SFP) is to find x ∈ C so that Ax ∈ Q, where C is a nonempty closed convex subset of Rn, Q is a nonempty closed convex subset of Rm, and A is a matrix from Rn into Rm. One of successful methods for solving the SFP is Byrne’s CQ algorithm. However, to carry out the CQ algorithm, it is required that the closed convex subsets are simple and that the matrix norm is kno...

Iterative algorithms based on the hybrid steepest descent method for the split feasibility problem

In this paper, we introduce two iterative algorithms based on the hybrid steepest descent method for solving the split feasibility problem. We establish results on the strong convergence of the sequences generated by the proposed algorithms to a solution of the split feasibility problem, which is a solution of a certain variational inequality. In particular, the minimum norm solution of the spl...