工程数学学报
工程數學學報
공정수학학보
CHINESE JOURNAL OF ENGINEERING MATHEMATICS
2011年
5期
598-608
,共11页
变分不等式%单调性%伪一致强制性%优化问题%算法收敛性
變分不等式%單調性%偽一緻彊製性%優化問題%算法收斂性
변분불등식%단조성%위일치강제성%우화문제%산법수렴성
variational inequalities%monotonicity%pseudo-Dunn property%optimization problems%convergence of algorithms
对于Lipschitz映射,一致强制性弱于强单调性,但强于单独的单调性.而伪一致强制性弱于一致强制性.本文给出了由双空间产生的映射的变分问题的并行算法.本质上,并行算法是利用辅助问题准则实行迭代计划.另外,本文还给出了这类算法的适当的收敛性条件,并证明了在伪一致强制条件下算法的收敛性.
對于Lipschitz映射,一緻彊製性弱于彊單調性,但彊于單獨的單調性.而偽一緻彊製性弱于一緻彊製性.本文給齣瞭由雙空間產生的映射的變分問題的併行算法.本質上,併行算法是利用輔助問題準則實行迭代計劃.另外,本文還給齣瞭這類算法的適噹的收斂性條件,併證明瞭在偽一緻彊製條件下算法的收斂性.
대우Lipschitz영사,일치강제성약우강단조성,단강우단독적단조성.이위일치강제성약우일치강제성.본문급출료유쌍공간산생적영사적변분문제적병행산법.본질상,병행산법시이용보조문제준칙실행질대계화.령외,본문환급출료저류산법적괄당적수렴성조건,병증명료재위일치강제조건하산법적수렴성.
For Lipschitz operators,the Dunn property is weaker than strong monotonicity,but is stronger than simple monotonicity.The pseudo-Dunn property is weaker than the Dunn property.In this paper,we consider a new parallel algorithm for an operator defined over the product of two spaces.Essentially,the idea is to use the auxiliary problem principle to perform the iterative schemes.In addition,other assumptions are proposed for the sequential version of the algorithm and we study the convergence under the pseudo-Dunn property assumption.
