变分不等式的并行算法(英文)

Parallel Algorithm for Variational Inequalities

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.

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.