关于极大强单调算子的不精确邻近点算法的收敛性分析

该文研究集值映象方程0∈T(z)的解的迭代逼近，其中T是极大强单调算子．设{x^k}与{e^k}是由不精确邻近点算法x^{k+1}+c_kT(x^{k+1})> x^k+e^{k+1}生成的序列，满足‖e^{k+1}‖≤η_k‖x^{k+1}_x^k‖, ∑^∞_{k=0}(η_k-1)<+∞且inf_(k≥0) η_k=μ≥1.在适当的限制下证明了，{x^k}收敛到T的一个根当且仅当 lim inf_{k→+∞} d(x^k,Z)=0，其中Z是方程0∈T(z)的解集

On the Convergence Analysis of Inexact Proximal Point Algorithms for Maximal Strongly Monotone Operators

The purpose of this paper is to study the iterative approximation of  solutions to the set valued mapping equation0∈T(z)  where T is a maximal strongly monotone  operator. Suppose that {x^k} and {e^k} are the sequences generated by  the inexact proximal  point algorithm x^{k+1}+c_kT(x^{k+1})> x^k+e^{k+1} such that ‖e^{k+1}‖≤η_k‖x^{k+1}_x^k‖, ∑^∞_{k=0}(η_k-1)<+∞ and inf_(k≥0) η_k=μ≥1 Under suitable restrictions the author proves that{x^k} converges to a root of T if and only if  liminf_{k→+∞} d(x^k,Z)=0