An Adaptive High Order Method for Finding Third-Order Critical Points of Nonconvex Optimization
报告时间： 2020年10月29日17:20-17:55
报告地点：数学学院203
报告人：江波 教授
单位：上海财经大学信息管理与工程学院
摘要：
It is well known that finding a global optimum is extremely challenging for nonconvex optimization. There are some recent efforts regarding the optimization methods for computing higher-order critical points, which can exclude the so-called degenerate saddle points and reach a solution with better quality. Desipte theoretical developments, the corresponding numerical experiments are missing. In this paper, we propose an implementable higher-order method, named adaptive high order method (AHOM), that aims to find the third-order critical points. This is achieved by solving an ``easier'' subproblem and incorporating the adaptive strategy of parameter-tuning in each iteration of the algorithm. The iteration complexity of the proposed method is established. Some preliminary numerical results are provided to show AHOM is able to escape the degenerate saddle points, where the second-order method could possibly get stuck.
报告人简介：
江波，上海财经大学博导，常聘（Tenured）教授，上海财经大学交叉科学研究院副院长，于2013年9月在美国明尼苏达大学工业与系统工程系获得博士学位，导师张树中教授。主要研究领域包括优化理论，组合投资优化，收益管理，信号处理等。在运筹优化领域的国际著名杂志Operations Research、Mathematics of Operations Research、Mathematical Programming、SIAM Journal on Optimization、SIAM Journal on Matrix Analysis and Applications等发表过多篇论文。主持过多项国家自然科学基金；荣获2015年上海财经大学学术新人奖、2016年申万宏源奖教金、2020中国运筹学会青年科技奖等荣誉
