极大单调算子的一个邻近点算法

A Proximal Point Algorithm of Maximal Monotone Operator in Reflexive Banach Spaces

设E是自反的Banach空间,T∶E→2E是极大单调算子.T-10≠.令x0∈E,yn=(J+λnT)-1xn+en,xn+1=J-1(αnJxn+(1-αn)Jyn),n≥0,λn>0,αn∈[0,1],本文研究了{xn}收敛性.

Let E be a reflexive Banach space and let T：E→2^E be a maximal monotone operator. T^-10≠Ф.{xn} is defined by x0∈E,yn=（J＋λnT）^-1xn＋en,xn＋1=J^-1（αnJxn＋（1-αn）Jyn）,n≥0,λn〉0,αn∈[0,1],In this paper,the convergence of {xn} is studied.