Partially Projective Algorithm for the Split Feasibility Problem with Visualization of the Solution Set

Abstract

This paper introduces a new three-step algorithm to solve the split feasibility problem. The main advantage is that one of the projective operators interferes only in the final step, resulting in less computations at each iteration. An example is provided to support the theoretical approach. The numerical simulation reveals that the newly introduced procedure has increased performance compared to other existing methods, including the classic CQ algorithm. An interesting outcome of the numerical modeling is an approximate visual image of the solution set.

New Iterative Algorithm for Solving Constrained Convex Minimization Problem and Split Feasibility Problem

“…The operator T = P C (I − λ∇f ) is well known to be nonexpansive (see [14,30] and the references therein). Several authors have have considered different iterative algorithm for constrained convex minimization problems (see [4,9,13,19,34] and the references therein). We now give our main results Theorem 8.2.…”

New Approach to Split Variational Inclusion Issues through a Three-Step Iterative Process

“…This inspires us to a change involving the TTP procedure. Moreover, we use the mapping U partially (once on every iteration step, as in [24,25]). Our procedure is defined as follows: for an arbitrarily initial point x 0 ∈ H 1 , the sequence {x n } is generated by…”

“…Feng et al combined the CQ algorithm with Thakur et al's [23] iteration procedure and obtained the so-called SFP-TTP projective algorithm. Similar ideas were developed in [24,25] using other three-step iteration procedures, resulting in the so-called partially projective algorithms. They benefit of an interesting upgrade: one of the projections is made only once per iteration.…”