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2021江苏省大规模复杂系统数值模拟实验室最优化论坛:Exploring the Data and Solution Sparsity in Large Scale Optimization Problems
报告人:孙德锋教授,香港理工大学 时间:2021年1月29日下午3:00 字号:


报告地点:线上 腾讯会议 ID 915 246 062

邀请人:孙海琳教授

报告摘要:It is widely believed by many researchers, in particular by those outside the traditional optimization community, that the second-order methods such as Newton’s method are no longer applicable for solving large scale optimization problems. This is partially true for optimization models that neither need a good optimal solution nor need to be solved quickly. In this talk, we shall first use large scale statistical optimization problems arising from machine learning to explain why the second-order methods, in particular the proximal point dual Newton algorithms (PPDNA), if wisely used, can be much faster than the first-order methods. The key point is to make use of the second-order sparsity of the optimal solutions in addition to the data sparsity so that, at each iteration, the computational costs of the second-order methods can be comparable or even lower than those of the first-order methods. Equipped with the PPDNA, we shall then introduce adaptive dimension-reduction methodologies to generate solution paths of very large sparse statistical optimization problems of particular importance in applications. Finally, we shall illustrate the high efficiency of our approach with extensive numerical results.

报告人简介:Professor Defeng Sun is currently Chair Professor of Applied Optimization and Operations Research at the Hong Kong Polytechnic University. He mainly publishes in convex and non-convex continuous optimization. Together with Professor Kim-Chuan Toh and Dr Liuqin Yang, he was awarded the triennial 2018 Beale--Orchard-Hays Prize for Excellence in Computational Mathematical Programming by the Mathematical Optimization Society. He served as editor-in-chief of Asia-Pacific Journal of Operational Research from 2011 to 2013 and he now serves as associate editor of Mathematical Programming, SIAM Journal on Optimization, Journal of the Operations Research Society of China, Journal of Computational Mathematics, and Science China: Mathematics. In 2020, he was elected as a Fellow of the societies SIAM and CSIAM.


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