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ISE Seminar Series Fall 2020

Title: Exploiting Second Order Sparsity in Big Data Optimization

Speaker: Kim-Chuan Toh, National University of Singapore (NUS)

Time: Tuesday, October 27, 11:00 AM to 12:00 PM

Join Zoom Meeting: https://lehigh.zoom.us/s/99527921266

Abstract:

In this talk, we shall demonstrate how second order sparsity (SOS) in important optimization problems such as sparse optimization models in machine learning, semidefinite programming, and many others can be exploited to design highly efficient algorithms. 

The SOS property appears naturally when one applies a semismooth Newton (SSN) method to solve the subproblems in an augmented Lagrangian method (ALM) designed for certain classes of structured convex optimization problems. With in-depth analysis of the underlying generalized Jacobians and sophisticated numerical implementation, one can solve the subproblems at surprisingly low costs. For lasso problems with sparse solutions, the cost of solving a single ALM subproblem by our second order method is comparable or even lower than that in a single iteration of many first order methods.

Consequently, with the fast convergence of the SSN based ALM, we are able to solve many challenging large scale convex optimization problems in big data applications efficiently and robustly.

This talk is based on joint work with Xudong Li (Fudan U.) and Defeng Sun (PolyU).

Bio:

Dr Toh is a Professor in the Department of Mathematics at the National University of Singapore (NUS). He obtained his BSc degree in Mathematics from NUS and PhD degree in Applied Mathematics from Cornell University.

He works extensively on convex programming, particularly large-scale matrix optimization problems such as semidefinite programming, and structured convex problems arising from machine learning and statistics.

He is currently an Area Editor for Mathematical Programming Computation, an Associate Editor for SIAM Journal on Optimization, Mathematical Programming, and ACM Transactions on Mathematical Software. He received the 2017 Farkas Prize and the 2018 triennial Beale-Orchard Hays Prize. He is also a Fellow of the Society for Industrial and Applied Mathematics.