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20201029 江波 An Adaptive High Order Method for Finding Third-Order Critical Points of Nonconvex Optimization

發布時間:2020-10-23 12:56    瀏覽次數:    來源:

An Adaptive High Order Method for Finding Third-Order Critical Points of Nonconvex Optimization


報告時間: 2020102917:20-17:55




報告人:江波 教授






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.



江波,上海財經大學博導,常聘(Tenured)教授,上海財經大學交叉科學研究院副院長,于20139月在美國明尼蘇達大學工業與系統工程系獲得博士學位,導師張樹中教授。主要研究領域包括優化理論,組合投資優化,收益管理,信號處理等。在運籌優化領域的國際著名雜志Operations Research、Mathematics of Operations Research、Mathematical Programming、SIAM Journal on Optimization、SIAM Journal on Matrix Analysis and Applications等發表過多篇論文。主持過多項國家自然科學基金;榮獲2015年上海財經大學學術新人獎、2016年申萬宏源獎教金、2020中國運籌學會青年科技獎等榮譽


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