The multiple-set split feasibility problem requires finding a point closest to a family of closed convex sets in one space such that its image under a linear transformation will 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 the solutions in the domain of a linear operator as well as in the operator’s range. It generalizes the convex feasibility problem as well as the two-set split feasibility problem. In this paper, we will review and report some recent results on iterative approaches to the multiple-set split feasibility problem.
"Applications of Fixed-Point and Optimization Methods to the Multiple-Set Split Feasibility Problem." J. Appl. Math. 2012 (SI03) 1 - 21, 2012. https://doi.org/10.1155/2012/927530