Efficient computation of the nearest polynomial by linearized alternating direction method
作者：
Highlights：
• This paper proposes an efficient algorithm following the framework of linearized alternating direction method with adaptive penalty for computing the nearest polynomial in the real case.
• Global convergence of the proposed algorithm is established under a mild assumption. Its convergence rate is also revealed in an ergodic sense by using a simple optimality measure.
• Solutions to the ℓp,q -norm regularized subproblems are discussed in details. Especially for the case of ℓp,q, we develop a projection-based primal-dual method (PPD) incorporating a root-finding procedure.
摘要
•This paper proposes an efficient algorithm following the framework of linearized alternating direction method with adaptive penalty for computing the nearest polynomial in the real case.•Global convergence of the proposed algorithm is established under a mild assumption. Its convergence rate is also revealed in an ergodic sense by using a simple optimality measure.•Solutions to the ℓp,q -norm regularized subproblems are discussed in details. Especially for the case of ℓp,q, we develop a projection-based primal-dual method (PPD) incorporating a root-finding procedure.
论文关键词：Empirical polynomial,Nearest polynomial,ℓp,q norm,Real zero,Linearized alternating direction method
论文评审过程：Received 18 July 2020, Accepted 26 November 2020, Available online 14 December 2020, Version of Record 14 December 2020.
论文官网地址：https://doi.org/10.1016/j.amc.2020.125860
