Abstract
In this paper, we present an extended alternating proximal penalization algorithm for the modified multiple-sets feasibility problem. For this method, we first show that the sequences generated by the algorithm are summable, which guarantees that the distance between two adjacent iterates converges to zero, and then we establish the global convergence of the algorithm provided that the penalty parameter tends to zero.
Highlights
1 Introduction The multiple-sets split feasibility problem, abbreviated as MSFP, is to find a point closest to the intersection of a family of some closed and convex sets in one space, such that its image under a linear operator is closest to the intersection of another family of some closed and convex sets in the image space
The MSFP consists in finding a point x∗ such that s t x∗ ∈ Ci and Ax∗ ∈ Qj, i=1 j=1 (1.1)
We first show that the sequences generated by our algorithm are summable, which guarantees that the distance between two adjacent iterates converges to zero, and we establish the global convergence of the algorithm provided that the penalty parameter tends to zero
Summary
The multiple-sets split feasibility problem, abbreviated as MSFP, is to find a point closest to the intersection of a family of some closed and convex sets in one space, such that its image under a linear operator is closest to the intersection of another family of some closed and convex sets in the image space. 3, we present a new method for solving the split problem and establish its convergence. 2 Preliminaries we first present some definitions and recall some existing conclusions which will be used in the subsequent analysis.
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