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《Adaptive scaling damped BFGS method without gradient Lipschitz continuity》学术讲座

发布时间: 2022-11-21 21:50:29

报告人:广西大学袁功林教授(邀请人:谭露琳)

时间:2022-11-25 10:00-11:00

腾讯会议:511-424-402


报告人简介:

       袁功林,广西大学数学与信息科学学院教授,博导,副院长,广西应用数学中心常务副主任,国家一流专业(数学与应用数学)负责人;主要研究优化理论与方法及其应用,主持国家基金2项、广西杰出青年基金1项、广西自然科学重点基金1项、中央主导地方科技发展基金1项、广西科技基地和人才专项基金1项、广西面上项目1项;宝钢教育奖,广西十百千第二层次人选,广西特聘青年专家;以第一或通讯作者发表SCI论文60余篇,如COAP、JOTA、JCAM等优化和计算期刊、“热点”2篇、“高被引”6篇、出版学术专著2部;获得广西自然科学二等奖2项;中国数学会理事、中国数学规划分会理事、广西数学会常务理事、广西运筹学会副理事长。


摘要:

       The Broyden–Fletcher–Goldfarb–Shanno (BFGS) method plays an important role among the quasi-Newton algorithms for nonconvex and unconstrained optimization problems. However, in the proof of global convergence, BFGS-type methods generally need to assume that the gradient of the objective function is Lipschitz continuous. This issue prompts us to try to find quasi-Newton method for gradient non-Lipschitz continuous and nonconvex optimization based on the classical BFGS formula. In this paper, we propose an adaptive scaling damped BFGS method for gradient non-Lipschitz continuous and nonconvex problems. With Armijo or Weak Wolfe–Powell (WWP) line search, global convergence can be obtained. Under suitable conditions the convergence rate is superlinear with WWP-type line search. Applications of the given algorithms include the tested optimization problems, which turn out the proposed method is powerful and promising.