题    目：Inexact Proximal Newton Method for Nonconvex Composite Minimization

报告人：朱红 副教授

单    位：江苏大学

时    间：2025年5月27日 19:00-22:00

地    点：数学与统计学院 106研讨室

摘    要：This report presents an inexact proximal Newton method along with its stochastic block-coordinate variant for solving nonconvex composite optimization problems. For the deterministic algorithm, we establish: (i) a global convergence rate of order \(\mathcal{O}(k^{-1/2}) with respect to the minimal norm of the KKT residual mapping, and (ii) a local superlinear convergence rate for the sequence generated by the algorithm under the assumption of higher-order metric \(q\)-subregularity. For the stochastic variant, we prove that, under appropriate sampling conditions, the fundamental convergence guarantees align with those of the deterministic case. Both versions of the method incorporate a unit step size combined with the Lipschitz constant of the gradient of the smooth component. In addition, we present algorithms for both versions that adopt a unit step size in combination with the Lipschitz constant of the gradient of the smooth component.

简    介：朱红，江苏大学副教授，硕士生导师。2016年博士毕业于香港浸会大学。主要研究方向为非线性优化及其应用。研究兴趣包括二阶算法，对偶四元数理论及应用。在 IEEE Trans. Image. Proc., SIAM J. Image. Sci., J. Sci. Comput., Inverse Prob. 等期刊发表论文20余篇，主持国家自然科学基金面上项目、青年项目、江苏省自然科学基金青年项目等。