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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 $x^*\in C\equiv\bigcap^t_{i=1} C_i\quad\text{such that}\quad x^*\in Q\equiv\bigcap^r_{j=1} Q_j,$ where $$A$$ is a given $$(M\times N)$$-matrix, $$C_i$$, $$\forall i= 1,\dots, t$$ are non-empty closed convex sets in $$\mathbb{R}^N$$, and $$Q_j$$, $$\forall j= 1,\dots, r$$ are non-empty closed convex sets in $$\mathbb{R}^M$$.
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

##### MSC:
 65K05 Numerical mathematical programming methods 49J40 Variational inequalities
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