We study the multiple-sets split feasibility problem that requires to find 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. By casting the problem into an equivalent problem in a suitable product space we are able to present a simultaneous subgradients projections algorithm that generates convergent sequences of iterates in the feasible case. We further derive and analyze a perturbed projection method for the multiple-sets split feasibility problem and, additionally, furnish alternative proofs to two known results.
Bibliographical noteFunding Information:
This work was supported by grant No. 2003275 of the United States–Israel Binational Science Foundation (BSF), by a National Institutes of Health (NIH) grant No. HL70472 and by grant No. 522/04 of the Israel Science Foundation (ISF) and was partially done at the Center for Computational Mathematics and Scientific Computation (CCMSC) in the University of Haifa.
- Averaged operators
- Multiple-sets split feasibility
- Perturbed projections
- Proximity function
- Subgradient projections
ASJC Scopus subject areas
- Applied Mathematics