New shrinking iterative methods for infinite families of monotone operators in a Banach space, computational experiments and applications

Journal of inequalities and applications

article

Li Wei¹  Rui Chen¹  Yanan Zhang¹  Ravi P. Agarwal² 

[1] School of Mathematics and Statistics, Hebei University of Economics and Business;Department of Mathematics, Texas A & M University—Kingsville

关键词: Lyapunov functional;    Monotone operators;    Shrinking iterative methods;    Convex minimization problems;    Variational inequalities;    Visual Basic Six;   

DOI  :  10.1186/s13660-020-02330-y

学科分类：电力

来源: SpringerOpen

【 摘 要 】

New shrinking iterative algorithms for approximating common zeros of two infinite families of maximal monotone operators in a real uniformly convex and uniformly smooth Banach space are designed. Two steps of multiple choices can be made in the new iterative algorithms, two groups of interactive containment sets $C_{n}$ and $Q_{n}$ are constructed and computational errors are considered, which are different from the previous ones. Strong convergence theorems are proved under mild assumptions and some new proof techniques can be found. Computational experiments for some special cases are conducted to show the effectiveness of the iterative algorithms and meanwhile some inequalities are proved to guarantee the strong convergence. Moreover, the applications of the abstract results on convex minimization problems and variational inequalities are exemplified.

【 授权许可】

CC BY