北京科技大學(xué)70周年校慶學(xué)術(shù)活動(dòng)——袁亞湘院士
報(bào)告題目：Least H^2 norm updating quadratic model for derivative-free trust region algorithms
報(bào)告人：袁亞湘 院士
報(bào)告時(shí)間：2022年4月22日 星期五15：00
會(huì)議形式：騰訊會(huì)議：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(bào)告人簡(jiǎn)介：
袁亞湘，中國科學(xué)院院士，中科院數(shù)學(xué)與系統(tǒng)科學(xué)研究院研究員。現(xiàn)任全國政協(xié)常委、中國科協(xié)副主席、國際工業(yè)與應(yīng)用數(shù)學(xué)聯(lián)合會(huì)主席、發(fā)展中國家科學(xué)院院士、巴西科學(xué)院通訊院士、美國數(shù)學(xué)會(huì)首屆會(huì)士、美國工業(yè)與應(yīng)用數(shù)學(xué)學(xué)會(huì)會(huì)士。
袁亞湘院士在非線性優(yōu)化計(jì)算方法、信賴域方法、擬牛頓方法、共軛梯度法等領(lǐng)域做出了突出貢獻(xiàn)，1999年在國際工業(yè)與應(yīng)用數(shù)學(xué)大會(huì)上做一小時(shí)報(bào)告，2014年被國際數(shù)學(xué)聯(lián)盟邀請(qǐng)?jiān)陧n國舉辦的國際數(shù)學(xué)家大會(huì)上做45分鐘報(bào)告。袁亞湘院士曾獲“中國科學(xué)院青年科學(xué)家獎(jiǎng)”一等獎(jiǎng)、首屆“馮康科學(xué)計(jì)算獎(jiǎng)”、第三屆“中國青年科學(xué)家獎(jiǎng)”、“國家杰出青年基金”、“中國十大杰出青年”、科技部“國家重點(diǎn)實(shí)驗(yàn)室計(jì)劃先進(jìn)個(gè)人獎(jiǎng)”、“國家自然科學(xué)獎(jiǎng)”二等獎(jiǎng)、中國數(shù)學(xué)會(huì)“陳省身數(shù)學(xué)獎(jiǎng)”、發(fā)展中國家科學(xué)院數(shù)學(xué)獎(jiǎng)、中國工業(yè)與應(yīng)用數(shù)學(xué)學(xué)會(huì)“蘇步青獎(jiǎng)”、“何梁何利科技進(jìn)步獎(jiǎng)”以及美國工業(yè)與應(yīng)用數(shù)學(xué)學(xué)會(huì)“杰出貢獻(xiàn)獎(jiǎng)”等。