Dual Newton Proximal Point Algorithm for Solution Paths of the L1-Regularized Logistic Regression

：刘勇进（福州大学）
：2023-02-16 15:40
：厦大海韵园实验楼105报告厅

报告人：刘勇进（福州大学）

时  间：2023年2月16日下午15:40-16:20

地  点：厦大海韵园实验楼105报告厅

内容摘要:

The L1-regularized logistic regression is a widely used statistical model in data classification. Though there are many algorithms for solving this problem in the literature, most of them are adapted to its one-variable equivalence problem and few solve the two-variable problem directly. In this talk, we propose a dual Newton method based proximal point algorithm (PPDNA) to solve the L1-regularized logistic regression problem with bias term. Theoretical results show that the global and asymptotically superlinear local convergence of the PPDNA holds under mild conditions. The computational cost of the semismooth Newton (Ssn) algorithm for solving subproblems in the PPDNA can be effectively reduced by fully exploiting the second-order sparsity of the problem. We also design an adaptive sieving (AS) strategy to generate solution paths for the L1-regularized logistic regression problem, where each subproblem in the AS strategy is solved by the PPDNA. This strategy utilizes active set constraints to reduce the number of variables in the problem, thereby speeding up the PPDNA for solving a series of problems. Numerical experiments demonstrate the superior performance of the PPDNA in comparison with some state-of-the-art algorithms and the efficiency of the AS strategy combined with the PPDNA for generating solution paths.

个人简介：

刘勇进，福州大学数学与统计学院教授、博士生导师、院长，福建省省级人才，担任福建省应用数学中心（福州大学）主任。研究兴趣主要包括：最优化理论、方法与应用，大规模数值计算，统计优化等，研究成果在包括Mathematical Programming (Series A)、SIAM Journal on Optimization、SIAM Journal on Scientific Computing等学术期刊上发表。主持国家自然科学基金4项（面上项目3项、青年基金1项），主持其他部省级纵向科研项目5项。现任中国统计学会理事、中国运筹学会学术交流委员会委员、中国运筹学会数学规划分会理事、中国运筹学会智能工业数据解析与优化分会理事。