报告题目 ：Homogeneous Second-Order Descent Framework: A Fast Alternative to Newton-Type Methods

报 告 人： 江波 教授 （上海财经大学）

报告时间：2024年7月24日（周三）10：00-11：30

报告地点：数学科学学院115（大报告厅）

校内报告联系人：刘永朝 教授  联系方式：84708354

报告摘要：This talk proposes a homogeneous second-order descent framework (HSODF) for nonconvex and convex optimization based on the generalized homogeneous model (GHM). In comparison to the Newton steps, the GHM can be solved by extremal symmetric eigenvalue procedures and thus grant an advantage in ill-conditioned problems. Moreover, GHM extends the ordinary homogeneous model (OHM) to allow adaptiveness in the construction of the aggregated matrix. Consequently, HSODF is able to recover some well-known second-order methods, such as trust-region methods and gradient regularized methods, while maintaining comparable iteration complexity bounds. We also study two specific realizations of HSODF. One is adaptive HSODM, which has a parameter-free $O(\epsilon^{-3/2})$ global complexity bound for nonconvex second-order Lipschitz continuous objective functions. The other one is homotopy HSODM, which is proven to have a global linear rate of convergence without strong convexity. The efficiency of our approach to ill-conditioned and high-dimensional problems is justified by some preliminary numerical results.

报告人简介： 江波，美国明尼苏达大学博士,上海财经大学信息管理与工程学院长聘教授，博士生导师，副院长。国家高层次青年人才计划入选者，上海市高层次人才，国家自然科学基金重大项目课题负责人。主要研究方向为：运筹优化、收益管理、机器学习等。有10多篇论文发表于运筹优化与机器学习的国际顶级期刊《Operations Research》、《Mathematics of Operations Research》、《Mathematical Programming》、《SIAM Journal on Optimization》、《INFORMS Journal on Computing》、《Journal of Machine Learning Research》。获得了中国运筹学会青年科技奖、上海市自然科学奖二等奖、宝钢优秀教师奖，上海市教学成果一等奖等荣誉。