极大单调算子零点的投影算法

设计了一种新的投影迭代算法,在实光滑、一致凸Banach空间中,利用Lyapunov泛函与广义投影映射等技巧,证明了迭代序列强收敛于极大单调算子的零点,并将此迭代算法加以推广,研究了有限个极大单调算子公共零点的迭代收敛性.

Projection Scheme for Zero Points of Maximal Monotone Operators

A new projection scheme is introduced and is proved to be strongly convergent to zero points of maximal monotone operators in a real smooth and uniformly convex Banach space by using the techniques of Lyapunov functional and generalized projection operator,etc.Later,it is extended to the case of approximating common zero points of finite maximal monotone operators.