报告题目：Least H^2 norm updating quadratic model for derivative-free trust region algorithms
报告人：袁亚湘 院士
報告時間：2022年4月22日 星期五15：00
会议形式：腾讯会议：627 684 677
摘要：
Derivative-free optimization problems are optimization problems that derivative information is not available or very difficult to obtain. Such optimization problems are widely seem in many real applications. Therefore, it is very important to construct efficient derivative-free optimization algorithms, namely numerical algorithms for solving optimization problems without using derivatives. One particular class of derivative-free optimization algorithms are trust region algorithms based on quadratic models by under-determined interpolation. The difference in updating the quadratic model from iteration to iteration will give different algorithms. In this talk, we propose a new algorithm that updates the quadratic model by minimizing the H^2 norm of the difference between quadratic models. Motivation for using the H^2 norm is given and theoretical properties of our new update technique are also presented. Finally, numerical results of our new algorithms are given to show the efficiency of our algorithm.
joint work with Pengcheng Xie
報告人簡介：
袁亚湘，中国科学院院士，中科院数学与系统科學研究院研究员。现任全国政协常委、中国科协副主席、国际工业与应用数学联合会主席、发展中国家科学院院士、巴西科学院通讯院士、美国数学会首届会士、美国工业与应用数学学会会士。
袁亞湘院士在非線性優化計算方法、信賴域方法、擬牛頓方法、共轭梯度法等領域做出了突出貢獻，1999年在國際工業與應用數學大會上做一小時報告，2014年被國際數學聯盟邀請在韓國舉辦的國際數學家大會上做45分鍾報告。袁亞湘院士曾獲“中國科學院青年科學家獎”一等獎、首屆“馮康科學計算獎”、第三屆“中國青年科學家獎”、“國家傑出青年基金”、“中國十大傑出青年”、科技部“國家重點實驗室計劃先進個人獎”、“國家自然科學獎”二等獎、中國數學會“陳省身數學獎”、發展中國家科學院數學獎、中國工業與應用數學學會“蘇步青獎”、“何梁何利科技進步獎”以及美國工業與應用數學學會“傑出貢獻獎”等。