Variable projection algorithms with sparse constraint for separable nonlinear models  

作　　者：Hui-Lang Xu Guang-Yong Chen Si-Qing Cheng Min Gan Jing Chen 

机构地区：[1]College of Computer and Data Science,Fuzhou University,Fuzhou,350116,Fujian,China [2]Fujian Key Laboratory of Network Computing and Intelligent Information Processing,Fuzhou University,Fuzhou,350116,Fujian,China [3]Key Laboratory of Intelligent Metro of Universities in Fujian,Fuzhou University,Fuzhou,350116,Fujian,China [4]Engineering Research Center of Big Data Intelligence,Ministry of Education,Fuzhou University,Fuzhou,350116,Fujian,China [5]School of Science,Jiangnan University,Wuxi,214122,Jiangsu,China

出　　处：《Control Theory and Technology》2024年第1期135-146,共12页控制理论与技术（英文版）

基　　金：supported in part by the National Nature Science Foundation of China(Nos.62173091,62073082);in part by the Natural Science Foundation of Fujian Province(No.2023J01268);in part by the Taishan Scholar Program of Shandong Province.

摘　　要：Separable nonlinear models are widely used in various fields such as time series analysis, system modeling, and machine learning, due to their flexible structures and ability to capture nonlinear behavior of data. However, identifying the parameters of these models is challenging, especially when sparse models with better interpretability are desired by practitioners. Previous theoretical and practical studies have shown that variable projection (VP) is an efficient method for identifying separable nonlinear models, but these are based on \(L_2\) penalty of model parameters, which cannot be directly extended to deal with sparse constraint. Based on the exploration of the structural characteristics of separable models, this paper proposes gradient-based and trust-region-based variable projection algorithms, which mainly solve two key problems: how to eliminate linear parameters under sparse constraint;and how to deal with the coupling relationship between linear and nonlinear parameters in the model. Finally, numerical experiments on synthetic data and real time series data are conducted to verify the effectiveness of the proposed algorithms.

关 键 词：Variable projection(VP) Non-smooth constraint Separable nonlinear models 

分 类 号：O17[理学—数学]