学术动态 | 讲座预告

报告摘要

Large-scale optimization problems arising from data science and statistics often look for optimal solutions with certain structured sparsity properties. In this talk, we shall introduce a dual semismooth Newton based proximal point algorithm (PPDNA) to solve such problems and explain how our method can be much more efficient than various first-order methods. The key idea is to make use of the second-order sparsity of the solutions, in addition to data sparsity, to make the per-iteration cost of our second-order method to be as low as that of first-order methods.  We demonstrate that by incorporating the PPDNA within an adaptive sieving framework, we can efficiently generate the solution paths of large-scale problems corresponding to a sequence of regularization parameters. We shall illustrate the high efficiency of our approach on several popular models including convex clustering, lasso, and exclusive lasso.

报告人简介

Kim-Chuan Toh is currently a Chair Professor in the Department of Mathematics at the National University of Singapore. He works extensively on convex programming, particularly large-scale matrix optimization problems such as semidefinite programming and sparse optimization problems arising from data science and machine learning. Currently he serves as a co-Editor for Mathematical Programming, an Area Editor for Mathematical Programming Computation, and an Associate Editor for several journals including SIAM J. Optimization and Operations Research. He received the Farkas Prize in 2017 from the INFORMS Optimization Society, and the triennial Beale-Orchard Hays Prize in 2018 and Pual Tseng Memorial Lectureship in 2024 from the Mathematical Optimization Society. He is a Fellow of the Society for Industrial and Applied Mathematics, and a Fellow of the Singapore National Academy of Science. 

报告摘要

网络设计在电信、交通、生产制造等行业中有着重要的应用，随着业务规模的迅速增长，如何基于现有网络进行扩容成为了一个重要的管理决策问题。基于电信网络的业务场景，考虑流量是否可分的限制，研究了一类多商品流网络扩容问题，即在满足不同服务的流量需求、容量限制和流量分割限制等约束的同时，进行扩容和流量分配决策，实现总成本最小化。基于对问题结构的分析，分别建立了基于弧流量和基于路径流量的数学模型，并设计了求解该问题的精确算法。重点研究了关键子问题的快速求解算法、有效不等式及快速分离与下界提升、基于流量转移的局部搜索与上界改进，这些关键设计使得算法运行高效，并在计算实验中得到验证。研究成果有助于提升改进服务网络设计及扩容升级规划的管理决策，并提供高效算法技术支持。

报告人简介

Kim-Chuan Toh is currently a Chair Professor in the Department of Mathematics at the National University of Singapore. He works extensively on convex programming, particularly large-scale matrix optimization problems such as semidefinite programming and sparse optimization problems arising from data science and machine learning. Currently he serves as a co-Editor for Mathematical Programming, an Area Editor for Mathematical Programming Computation, and an Associate Editor for several journals including SIAM J. Optimization and Operations Research. He received the Farkas Prize in 2017 from the INFORMS Optimization Society, and the triennial Beale-Orchard Hays Prize in 2018 and Pual Tseng Memorial Lectureship in 2024 from the Mathematical Optimization Society. He is a Fellow of the Society for Industrial and Applied Mathematics, and a Fellow of the Singapore National Academy of Science.