Efficient ADMM-Based Algorithm for Regularized Minimax Approximation

• Published in: IEEE signal processing letters Vol. 30; pp. 210 - 214
• Main Authors: Shentu, Xuanyue, Lai, Xiaoping, Wang, Tianlei, Cao, Jiuwen
• Format: Journal Article
• Language: English
• Published: New York IEEE 2023; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: ADMM; Algorithms; Approximation; Approximation algorithms; Computational geometry; Convex functions; Convexity; digital filter design; Digital filters; Finite impulse response filters; Machine learning; Machine learning algorithms; Mathematical analysis; Minimax approximation; Minimax technique; Neural networks; Optimization; Programming; Signal processing algorithms
• ISSN: 1070-9908; 1558-2361
• DOI: 10.1109/LSP.2023.3253053

Minimax approximations have found many applications but are lack of efficient solution algorithms for large-scale problems. Based on the alternating direction method of multipliers (ADMM) for convex optimization, this letter presents an efficient scalarwise algorithm for a regularized minimax approximation problem. The ADMM-based algorithm is then applied in the minimax design of two-dimensional (2-D) digital filters and the training of randomized neural networks for regression on a realworld benchmark dataset. Experimental results demonstrate the fast convergence rate and low computational complexity of the proposed algorithm, as well as the good approximation/prediction performance of the learned approximation model.