This paper studies new accelerated optimization algorithms and applied the algorithms to prediction of breast cancer through machine learning approach. To do this, we first introduce new fast CQ algorithms and obtain weak convergence results. In one of our proposed algorithms (inertial-type CQ Algorithm), the inertial choice could be negative and even greater than 1 with no on-line rule imposed in order to obtain convergence results. This is a major improvement over other inertial-type algorithms in the literature where inertial choices are restrictive to [0 ,1) and on-line rule is imposed. Then we validate the applicability of the proposed CQ algorithms to real-life applications by predicting breast cancer by updating the optimal weight in machine learning. We use the mammographic mass dataset from the UC Irvine machine learning repository that is available on the UCI website as a training set to show the superiority of our algorithms over existing ones in the literature.

In this paper, we solve a common problem of split null inclusion problem, variational inequality and hierarchical fixed point problem for nonexpansive and quasi-nonexpansive mappings using hybrid projective method. Under suitable conditions in a real Hilbert space, strong convergent theorems are proved. Further, we give an example for supporting our main result in infinitely dimensional spaces and show the efficiency of the algorithm by applying to solve the signal recovery problem.