十大网投靠谱网站学术报告
On the linear convergence of non-Euclidean gradient method without convexity and gradient Lipschitz continuity
陈加伟 教授
（西南大学数学与统计学院）
报告时间：2021年4月21日下午3:00-4:00
报告地点：沙河校区J1-110
报告摘要：The gradient method is well known to globally converge linearly when the objective function is strongly convex and admits a Lipschitz continuous gradient. In many applications, both assumptions are often too stringent, precluding the use of gradient methods. In the early 1960s, after the amazing breakthrough of Łojasiewicz on gradient inequalities, it was observed that uniform convexity assumptions could be relaxed and replaced by these inequalities. On the other hand, very recently, it has been shown that the Lipschitz gradient continuity can be lifted and replaced by a class of functions satisfying a non-Euclidean descent property expressed in terms of a Bregman distance. In this note, we combine these two ideas to introduce a class of non-Euclidean gradient-like inequalities, allowing to prove linear convergence of a Bregman gradient method for nonconvex minimization, even when neither strong convexity nor Lipschitz gradient continuity holds.
报告人简介：陈加伟，博士，教授，重庆市运筹学学会常务理事，重庆市数学学会理事，担任美国“数学评论”评论员。2013年博士毕业于武汉大学，同年7月入职西南大学担任副教授，并于2018年7月晋升为教授。曾获教育部博士研究生学术新人奖。曾多次到韩国国立庆尚大学、加拿大英属哥伦比亚大学、西蒙菲莎大学，台湾中山大学与高雄医学大学展开合作研究。研究方向为最优化理论及应用，具体涉及多目标优化、双层规划、变分不等式、平衡问题等理论与算法研究。科研成果主要发表SIOPT、COA、JGO、JOTA、 MMOR、 KBS、中国科学：信息科学(英文版)等专业学术期刊上。主持国家自然科学基金面上项目与青年项目、中国博士后科学基金、重庆市自然科学基金项目各一项，主研3项国家自然科学基金研究项目。
邀请人： 谢家新
