Applications of Fixed-Point and Optimization Methods to the Multiple-Set Split Feasibility Problem

Abstract EN

The multiple-set split feasibility problem requires finding a point closest to afamily of closed convex sets in one space such that its image under a linear transformationwill be closest to another family of closed convex sets in the image space.

It can be a model for many inverse problems where constraints are imposed on thesolutions in the domain of a linear operator as well as in the operator’s range.

Itgeneralizes the convex feasibility problem as well as the two-set split feasibilityproblem.

In this paper, we will review and report some recent results on iterative approachesto the multiple-set split feasibility problem.