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具有叠加扰动的改进向前-向后分裂中点法求解两类无穷增生映射之和及其应用

Modified forward-backward splitting midpoint method with superposition perturbations for the sum of two kinds of infinite accretive mappings and its applications.

作者信息

Wei Li, Duan Liling, Agarwal Ravi P, Chen Rui, Zheng Yaqin

机构信息

School of Mathematics and Statistics, Hebei University of Economics and Business, 47 Xuefu Road, Shijiazhuang, China.

Department of Mathematics, Texas A&M University-Kingsville, Kingsville, TX 78363 USA.

出版信息

J Inequal Appl. 2017;2017(1):227. doi: 10.1186/s13660-017-1506-9. Epub 2017 Sep 18.

DOI:10.1186/s13660-017-1506-9
PMID:28989255
原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC5603715/
Abstract

In a real uniformly convex and -uniformly smooth Banach space, a modified forward-backward splitting iterative algorithm is presented, where the computational errors and the superposition of perturbed operators are considered. The iterative sequence is proved to be convergent strongly to zero point of the sum of infinite m-accretive mappings and infinite [Formula: see text]-inversely strongly accretive mappings, which is also the unique solution of one kind variational inequalities. Some new proof techniques can be found, especially, a new inequality is employed compared to some of the recent work. Moreover, the applications of the newly obtained iterative algorithm to integro-differential systems and convex minimization problems are exemplified.

摘要

在一个实一致凸且一致光滑的巴拿赫空间中，提出了一种修正的前向后向分裂迭代算法，其中考虑了计算误差和扰动算子的叠加。证明了迭代序列强收敛到无穷多个m -增生映射和无穷多个[公式：见原文]-逆强增生映射之和的零点，该零点也是一类变分不等式的唯一解。可以发现一些新的证明技术，特别是与一些近期工作相比，采用了一个新的不等式。此外，还举例说明了新得到的迭代算法在积分微分系统和凸最小化问题中的应用。