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

Zhao, Jinling; Yang, Qingzhi

Inverse Probl. Sci. Eng. 21, No. 3, 537-546 (2013).

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.

Reviewer: Gabriela Cristescu (Arad)

MSC:

65K05	Numerical mathematical programming methods
90C25	Convex programming

Keywords:

multiple-sets split feasibility problem; projection method; separating hyperplane; relaxed projection method; convergence; numerical experiment

References:

[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