我们使用的概念，障碍为基础的平滑近似介绍[ C。B. Chua和Z. Li，A barrier-based smoothing邻近点法for NCP over closed凸锥，SIOPT 23（2），2010]，以扩展[B. Chen和N. Xiu，A global linear and local quadratic non-interior continuation method for nonlinear互补性问题based on Chen-Mangasarian smoothing functions，SIOPT 9（3），1999]到一般闭凸集上变分不等式的不精确非内部连续方法.为了处理高维问题，该方法中涉及的牛顿方程是不精确求解的。在适当的假设下，证明了该方法具有全局线性收敛性和局部超线性/平方收敛性.我们将此方法应用于非负正交图、半正定锥、多面体集、矩阵算子范数锥的上图和矩阵核范数锥的上图。
英文摘要：
We use the concept of barrier-based smoothing approximations introduced in [ C. B. Chua and Z. Li, A barrier-based smoothing proximal point algorithm for NCPs over closed convex cones, SIOPT 23(2), 2010] to extend the non-interior continuation method proposed in [B. Chen and N. Xiu, A global linear and local quadratic noninterior continuation method for nonlinear complementarity problems based on Chen-Mangasarian smoothing functions, SIOPT 9(3), 1999] to an inexact non-interior continuation method for variational inequalities over general closed convex sets. Newton equations involved in the method are solved inexactly to deal with high dimension problems. The method is proved to have global linear and local superlinear/quadratic convergence under suitable assumptions. We apply the method to non-negative orthants, positive semidefinite cones, polyhedral sets, epigraphs of matrix operator norm cone and epigraphs of matrix nuclear norm cone.
A Stochastic Block-coordinate Proximal Newton Method for Nonconvex Composite Minimization
School of Mathematical Sciences, Jiangsu University（江苏大学数学科学学院）；Center of Excellence for Generative AI, King Abdullah University of Science and Technology（阿卜杜拉国王科技大学生成式人工智能卓越中心）
Distributed Gradient-Regularized Newton Method: Scheduled Consensus and O(epsilon^{-1}) Global Iteration Complexity
Academy of Mathematics and Systems Science, Chinese Academy of Sciences（中国科学院数学与系统科学研究院）；University of Chinese Academy of Sciences（中国科学院大学）；Lawrence Berkeley National Laboratory（劳伦斯伯克利国家实验室）
