An inertial relaxed CQ algorithm with an application to the LASSO and elastic net. (3rd June 2021)

• Record Type: Journal Article
• Authors: Wang, Fenghui; Yu, Hai
• Is Part Of: Optimization. Volume 70:Number 5/6(2021)
• Page Start: 1101
• Page End: 1119
• Publication Date: 2021-06-03
• Subjects: Split feasibility problem -- relaxed CQ algorithm -- variable step-size; 47J25 -- 47J20 -- 49N45 -- 65J15; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2020.1763989
• Languages: English
• ISSNs: 0233-1934

Abstract

ABSTRACT: The relaxed CQ algorithm is a very efficient algorithm for solving the split feasibility problem (SFP) whenever the convex subsets involved are level subsets of given convex functions. It approximates the original convex subset by a sequence of half-spaces that overcomes the difficulties for calculating the projection onto original convex subsets. In this paper, we propose a new inertial relaxed algorithm in which we approximate the original convex subset by a sequence of closed balls instead of half spaces. Moreover, we construct a new variable step-size that does not need any prior information of the norm. We then establish the weak convergence of the proposed algorithm under two different assumptions. Experimental results in the LASSO and elastic net methods show that our algorithm has a better performance than other relaxed algorithms.