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Zbl 1185.65102
Zhang, Wenxing; Han, Deren; Li, Zhibao
A self-adaptive projection method for solving the multiple-sets split feasibility problem.
(English)
[J] Inverse Probl. 25, No. 11, Article ID 115001, 16 p. (2009). ISSN 0266-5611

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 $\bbfR^N$, and $Q_j$, $\forall j= 1,\dots, r$ are non-empty closed convex sets in $\bbfR^M$.\par 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 {\it B. S. He}, {\it H. Yang}, {\it Q. Meng} and {\it D. R. Han} [J. Optimization Theory Appl. 112, No. 1, 129--143 (2002; Zbl 0998.65066)] to problems with weaker conditions.
[K. Zimmermann]
MSC 2000:
*65K05 Mathematical programming (numerical methods)
49J40 Variational methods including variational inequalities

Keywords: variational inequalities; multiple-sets split feasibility problem; iterative projection methods

Citations: Zbl 0998.65066

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