Abstract
For the split feasibility problem, we propose a new type of solution method by introducing a new searching direction with fixed stepsize. Its global convergence is proved under a suitable condition. Preliminary numerical experiments show the efficiency of the proposed method.
Similar content being viewed by others
References
Bauschke H H, Borwein J M. On projection algorithms for solving convex feasibility problems. SIAM Review, 1996, 38: 367–426
Byrne C L. Bregman-Legendre multidistance projection algorithms for convex feasibility and optimization. In: Butnairu D, Censor Y, Reich S, eds. Inherently Parallel Algorithms in Feasibility and Optimization and Their Applications. Amsterdam: Elsevier, 2001, 87–100
Byrne C L. Iterative oblique projection onto convex sets and the split feasibility problem. Inverse Problems, 2002, 18: 441–453
Censor Y, Elfving T. A multiprojection algorithm using Bregman projections in a product space. Numerical Algorithms, 1994, 8: 221–239
Gafni E M, Bertsekas D P. Two-metric projection problems and descent methods for asymmetric variational inequality problems. Math Program, 1984, 53: 99–110
Qu B, Xiu N H. A note on the CQ algorithm for the split feasibility problem. Inverse Problems, 2005, 21: 1655–1665
Rockafellar R T. Convex Analysis. Princeton: Princeton University Press, 1970
Yang Q Z. The relaxed CQ algorithm solving the split feasibility problem. Inverse Problems, 2004, 20: 1261–1266
Zarantonello E H. Projections on convex sets in Hilbert space and spectral theory. In: Zarantonello E H, ed. Contributions to Nonlinear Functional Analysis. New York: Academic Press, 1971
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Zhang, H., Wang, Y. A new CQ method for solving split feasibility problem. Front. Math. China 5, 37–46 (2010). https://doi.org/10.1007/s11464-009-0047-z
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11464-009-0047-z