Banach空间中极大单调算子的一个邻近点算法

A Proximal Point Algorithm of Maximal Monotone Operator in Banach Spaces

设E是Banach空间,T∶E→2E*是极大单调算子,T-10≠ф.令x0∈E,yn=(J+λnT)-1xn+en,xn+1=J-1(αnJxn+(1-αn)Jyn),n0,λn>0,αn∈[0,1],文章研究了{xn}收敛性.

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