Abstract
In this paper, we first introduce the two-step intermixed iteration for finding the common solution of a constrained convex minimization problem, and also we prove a strong convergence theorem for the intermixed algorithm. By using our main theorem, we prove a strong convergence theorem for the split feasibility problem. Finally, we apply our main theorem for the numerical example.
The proximal split feasibility problem has been studied. A regularized method has been presented for solving the proximal split feasibility problem. Strong convergence theorem is given.
We establish strong convergence result of split feasibility problem for a family of quasi-nonexpansive multi-valued mappings and a total asymptotically strict pseudo-contractive mapping in infinite dimensional Hilbert spaces.
The purpose of this paper is to introduce an iterative algorithm of two sequences which depend on each other by using the intermixed method. Then, we prove a strong convergence theorem for solving fixed-point problems of nonlinear mappings and we treat two variational inequality problems which form an approximate modified generalized system of variational inequalities (MGSV). By using our main theorem, we obtain the additional results involving the split feasibility problem and the constrained convex minimization problem. In support of our main result, a numerical example is also presented.
An explicit iterative method with self-adaptive step-sizes for solving the split feasibility problem is presented. Strong convergence theorem is provided.
In this work, we introduce a modified inertial algorithm for solving the split common null point problem without the prior knowledge of the operator norms in Banach spaces. The strong convergence theorem of our method is proved under suitable assumptions. We apply our result to the split feasibility problem, split equilibrium problem and split minimization problem. Finally, we provide some numerical experiments including compressed sensing to illustrate the performances of the proposed method. The result presented in this paper improves and generalizes many recent important results in the literature.
In this paper, we study an iterative method for solving the multiple-set split feasibility problem: find a point in the intersection of a finite family of closed convex sets in one space such that its image under a linear transformation belongs to the intersection of another finite family of closed convex sets in the image space. In our result, we obtain a strongly convergent algorithm by relaxing the closed convex sets to half-spaces, using the projection onto those half-spaces and by introducing the extended form of selecting step sizes used in a relaxed CQ algorithm for solving the split feasibility problem. We also give several numerical examples for illustrating the efficiency and implementation of our algorithm in comparison with existing algorithms in the literature.
An intermixed iteration for constrained convex minimization problem and split feasibility problem
