Split Variational Inclusion Problem and Fixed Point Problem for Asymptotically Nonexpansive Semigroup with Application to Optimization Problem

S. H. Chang, L. C. Zhao, Z. L. Ma, G. Wang
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Abstract

The purpose of this paper is by using the shrinking projection method to introduce and study an iterative process to approximate a common solution of split variational inclusion problem and fixed point problem for an asymptotically nonexpansive semigroup in real Hilbert spaces. Further, we prove that the sequences generated by the proposed iterative method converge strongly to a common solution of split variational inclusion problem and fixed point problem for an asymptotically nonexpansive semigroup. As applications, we shall utilize the results to study the split optimization problem and the split variational inequality.
渐近非扩张半群的分裂变分包含问题和不动点问题及其在优化问题上的应用
本文的目的是利用收缩投影法,引入并研究了实数Hilbert空间中渐近非扩张半群的分裂变分包含问题和不动点问题的一个公解的迭代逼近过程。进一步证明了该迭代方法生成的序列强收敛于渐近非扩张半群的分裂变分包含问题和不动点问题的一个公共解。作为应用,我们将利用这些结果来研究分裂优化问题和分裂变分不等式。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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