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报告题目: Global and Local Convergence-Rate Analysis of an Inexact Newton Augmented Lagrangian Method for Zero-One Composite Optimization

报告人：戚厚铎（HOUDUO QI） 教授 香港理工大学

报告时间：2023年6月17日（周六） 下午16:30-17:30

报告地点：北航沙河校区主楼E404

线上腾讯会议号：278-872-959

Abstract：Zero-One Composite Optimization (0/1-COP) is a prototype of nonsmooth, nonconvex optimization problems and it has attracted much attention recently. Augmented Lagrangian Method (ALM) has stood out as a leading methodology for such problems. The main purpose of this paper is to extend the classical theory of ALM from smooth problems to 0/1-COP. We propose, for the first time, second-order optimality conditions for 0/1-COP. In particular, under a second-order sufficient condition (SOSC), we prove Q-linear convergence rate of the proposed ALM. In order to identify the subspace used in SOSC, we employ the proximal operator of the 0/1-loss function, leading to an active-set identification technique. Built around this identification process, we design practical stopping criteria for any algorithm to be used for the subproblem of ALM. We justify that Newton's method is an ideal candidate for the subproblem and it enjoys both global and quadratic convergence. Those considerations result in an inexact Newton ALM (iNALM) for 0/1-COP. The method of iNALM is unique in the sense that it is active-set based and it is inexact (hence more practical). SOSC plays an important in its R-linear convergence analysis. The numerical results on both simulated and real datasets show the fast running speed and high accuracy of iNALM when compared with several leading solvers (Joint work with Xiu Naihua and Zhang Penghe).

Bio: Houduo Qi received the BSc in Statistics from Peking University in 1990, MSc and PhD in Operational Research and Optimal Control, respectively from Qufu Normal University (1993) and the Institute of Applied Mathematics, Chinese Academy of Sciences (CAS) in 1996. He has been postdoctoral fellows at the Institute of Computational Mathematics, CAS, the Hong Kong Polytechnic University, and the University of New South Wales before joining the University of Southampton in 2004 as a lecturer in Operational Research, rising to Professor and Chair of Optimization. He is now a professor at the department of applied mathematics, the Hong Kong Polytechnic University.

He was awarded the prestigious Queen Elizabeth II Fellowship (QEII Fellow) by the Australian Research Council (2003) and Turing Fellow in 2019 by the Alan Turing Institute, UK’s national institute of data science. He is mainly interested in Mathematical Optimization, especially in matrix optimization with applications to finance and statistics. He is currently the area editor (Optimization) of Asia-Pacific Journal of Operational Research, associate editors for Mathematical Programming Computation, Computational Optimization and Applications, and Journal of Operations Research Society of China. From 2010, he has been a college member of Engineering and Physical Sciences Research Council, UK.