学术报告

题      目： Adaptive scaling damped BFGS method without gradient Lipschitz continuity

报  告  人：袁功林   教授  (邀请人：谭露琳 )

                               广西大学

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.