Alternated inertial simultaneous and semi-alternating projection algorithms for solving the split equality problem

Abstract

In this paper, we introduce the simultaneous and semi-alternating projection algorithms for solving the split equality problem by using a new choice of the step size and combining the alternated inertial technique. The weak convergence of the proposed algorithms is analyzed under standard conditions. Finally, a numerical example is presented to illustrate the efficiency and advantage of the proposed algorithms by comparing with other methods.

A self-adaptive forward-backward-forward algorithm for solving split variational inequalities

“…The prototype of split variational inequality considered in [8,20,24,41] is to seek a point x † such that x † ∈ Sol(C, φ) and A(x † ) ∈ Sol(Q, ψ), where A : C → Q is a bounded linear operator. The reason why we are interested in the split variational inequality is that it is an extension of the split feasibility problem ( [6]) arising from image denoising, signal processing and image reconstruction, see, [13,14,19,27,28,38,39,40] for more details.…”