Strong convergence of over-relaxed multi-parameter proximal scaled gradient algorithm and superiorization. (4th March 2021)

• Record Type: Journal Article
• Authors: Guo, Yanni; Zhao, Xiaozhi
• Is Part Of: Optimization. Volume 70:Number 3(2021)
• Page Start: 461
• Page End: 480
• Publication Date: 2021-03-04
• Subjects: Strong convergence -- bounded perturbation resilience -- proximal gradient algorithm -- over-relaxed -- convex minimization problem; 47H09 -- 49J45 -- 49M25 -- 65J22 -- 90C46; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2020.1722124
• Languages: English
• ISSNs: 0233-1934

Abstract

ABSTRACT: In this paper, we propose an over-relaxed proximal scaled gradient algorithm for solving the non-smooth composite optimization problem in Hilbert space. We prove the strong convergence and the bounded perturbation resilience of this algorithm under some mild conditions. We also list the superiorized version of the algorithm. We apply the algorithms to the l 1 − l 2 problem to illustrate the performance and validity. The numerical examples show that the over-relaxed algorithm can achieve fewer iteration steps and less running times in comparison to the under-relaxed algorithm, and that the superiorization algorithm has the minimum iterative steps among the three algorithms.