中国科学A辑(英文版)
中國科學A輯(英文版)
중국과학A집(영문판)
SCIENCE IN CHINA
2003年
2期
200-206
,共7页
proximal point algorithms%monotone operators%approximate methods
The problem concerned in this paper is the set-valued equation 0 ∈ T(z) where T is a maximal monotone operator. For given xk and βk ＞ 0, some existing approximate proximal point algorithms take xk+1 = xk such that xk +ek∈ xk + βkT(xk) and||ek|| ≤ηk||xk - xk||, where {ηk} is a non-negative summable sequence. Instead of xk+1 = xk, the new iterate of the proposing method is given by xk+1 = PΩ[xk - ek], where Ω is the domain of T and PΩ(@) denotes the projection on Ω. The convergence is proved under a significantly relaxed restriction supk＞0 ηk ＜ 1.
