Abstract
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.
| Original language | English |
|---|---|
| Pages (from-to) | 1244-1256 |
| Number of pages | 13 |
| Journal | Journal of Mathematical Analysis and Applications |
| Volume | 327 |
| Issue number | 2 |
| DOIs | |
| State | Published - 15 Mar 2007 |
Bibliographical note
Funding 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.
Keywords
- Averaged operators
- CQ-algorithm
- Multiple-sets split feasibility
- Perturbed projections
- Proximity function
- Subgradient projections
ASJC Scopus subject areas
- Analysis
- Applied Mathematics