论文标题
与Hölder连续Jacobians单调变化不平等的正规化牛顿方法
Regularized Newton Methods for Monotone Variational Inequalities with Hölder Continuous Jacobians
论文作者
论文摘要
本文考虑了解决霍尔德连续雅各布人解决单调变化不平等的问题。通过采用Hölder参数$ν$的知识，我们最多只能在$ \ Mathcal O（ε^{ - 2/（2+ν）}）$迭代中提出$ν$ regularized Newton方法，以获得$ε$ -ACCCRATE解决方案。在$ν$的情况下是未知的，我们建议在$ \ Mathcal O（ε^{ - 4/（3（1+ν））}）中的通用正规化牛顿法。
This paper considers the problems of solving monotone variational inequalities with Hölder continuous Jacobians. By employing the knowledge of Hölder parameter $ν$, we propose the $ν$-regularized extra-Newton method within at most $\mathcal O(ε^{-2/(2+ν)})$ iterations to obtain an $ε$-accurate solution. In the case of $ν$ is unknown, we propose the universal regularized extra-Newton method within $\mathcal O(ε^{-4/(3(1+ν))})$ iteration complexity.
