变分不等式的一种自适应算法

Self-adaptive algorithm for variational inequalities

提出求解定义在实Hilbert空间闭凸集上Lipschitz强单调变分不等式唯一解的一种自适应算法,即以一种自适应的方式在每一步迭代计算时确定计算格式中的迭代步长,无需计算或估计其中非线性算子的Lipschitz常数和强单调系数,从而使得该算法更容易实现。证明了算法的强收敛性。

A self-adaptive algorithm is proposed to solve the Lipschitz and strongly monotone variational inequality defined on a closed convex subset in a real Hilbert space.Since this method selects stepsizes via a selfadaptive way,i.e.,has no need to estimate the Lipschitz constant and strong monotone coefficient,its implementation is rather easy.Strong convergence of the algorithm is proved.