A simple projection method for solving the multiple-sets split feasibility problem. (English) Zbl 1285.65038

The multiple-sets split feasibility problem consists in finding a point in the intersection of a family of closed convex sets, which goes, by a linear transformation, into a point of the same type from the image space. This problem is approached, elaborating a practical projection method, which is faster and easier to implement than the already known techniques. The convergence of the method is accelerated by computing the best step-size for the current direction in each iteration. A relaxed projection scheme improves this technique, making it easier to implement. The theoretical foundation of the new method, together with few numerical experiments are included.


65K05 Numerical mathematical programming methods
90C25 Convex programming
Full Text: DOI


[1] DOI: 10.1088/0266-5611/18/2/310 · Zbl 0996.65048
[2] DOI: 10.1088/0266-5611/20/1/006 · Zbl 1051.65067
[3] DOI: 10.1007/BF02142692 · Zbl 0828.65065
[4] DOI: 10.1088/0266-5611/21/6/017 · Zbl 1089.65046
[5] DOI: 10.1088/0266-5611/25/11/115001 · Zbl 1185.65102
[6] DOI: 10.1088/0266-5611/27/3/035009 · Zbl 1215.65115
[7] DOI: 10.1088/0266-5611/21/5/009 · Zbl 1080.65033
[8] DOI: 10.1023/B:NUMA.0000021777.31773.c3 · Zbl 1056.65027
[9] Zarantonello EH, Contributions to Nonlinear Functional Analysis 20 (1971)
[10] DOI: 10.1088/0266-5611/20/4/014 · Zbl 1066.65047
[11] Rockafellar RT, Convex Analysis (1970) · Zbl 0932.90001
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