Efficient iterative method for SOAV minimization problem with linear equality and box constraints and its linear convergence

This study proposes an efficient algorithm for the sum-of-absolute-values (SOAV) minimization problem with linear equality and box constraints by exploiting alternating direction method of multipliers (ADMM). In the iteration of ADMM, efficient algorithms for the calculations of proximal points, which are the solutions of sub-problems and have great effects on the computation efficiency, are employed. By focusing on the dynamical structure of the iteration, the linear convergence of the proposed algorithm is proven. Furthermore, a practical application for mechanical system control with discrete-valued control illustrates the advantages of the proposed methods. (C) 2022 The Author(s). Published by Elsevier Ltd on behalf of The Franklin Institute.

Automated summary

This study proposes an efficient algorithm for solving the sum-of-absolute-values (SOAV) minimization problem with linear equality and box constraints using the alternating direction method of multipliers (ADMM). The algorithm employs efficient methods for calculating proximal points to improve computation efficiency. The study proves the linear convergence of the proposed algorithm and demonstrates its advantages through a practical application.