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A self-adaptive projection method for solving the multiple-sets split feasibility problem. (English) Zbl 1185.65102

The authors consider the following multiple-sets split feasibility problem: Find a vector

x * C i=1 t C i suchthatx * Q j=1 r Q j ,

where A is a given (M×N)-matrix, C i , i=1,,t are non-empty closed convex sets in N , and Q j , j=1,,r are non-empty closed convex sets in M .

A new method for solving this problem is proposed, which uses variable step-sizes unlike to other methods known from the literature, whcih use a fixed step-size. The m ethod is an extension and application of the method published by B. S. He, H. Yang, Q. Meng and D. R. Han [J. Optimization Theory Appl. 112, No. 1, 129–143 (2002; Zbl 0998.65066)] to problems with weaker conditions.

Reviewer: K. Zimmermann
65K05Mathematical programming (numerical methods)
49J40Variational methods including variational inequalities