Combining line search and trust-region methods for ℓ1-minimization. Issue 10 (3rd October 2018)

• Record Type: Journal Article
• Authors: Esmaeili, Hamid; Rostami, Majid; Kimiaei, Morteza
• Is Part Of: International journal of computer mathematics. Volume 95:Issue 10(2018)
• Page Start: 1950
• Page End: 1972
• Publication Date: 2018-10-03
• Subjects: ℓ1-minimization -- compressed sensing -- image deblurring -- shrinkage operation -- trust-region framework -- nonmonotone line search -- global convergence; 65K05 -- 90C25 -- 90C06 -- 94A08; Computers -- Periodicals; Numerical analysis -- Periodicals; Automation -- Periodicals; 004.0151
• DOI: 10.1080/00207160.2017.1346241
• Languages: English
• ISSNs: 0020-7160

Abstract

ABSTRACT: This study presents a new trust-region algorithm to solve theℓ 1 -minimization problem with applications to compressed sensing (CS) and image deblurring that will be augmented with a shrinkage operation to produce a new iteration whenever an approximated solution of the trust-region subproblem lies within one and iterate is successful, simultaneously. Otherwise, a nonmonotone Armijo-type line search strategy incorporates with shrinkage technique, which includes a convex combination of the maximum function value of some preceding iterates and the current function value. Therefore, the proposed approach takes advantages of both the effective trust-region and nonmonotone Armijo-type line search with a shrinkage operation. It is believed that selecting an appropriate shrinkage parameter according to a new procedure can improve the efficiency of our algorithm. The global convergence and the R-linear convergence rate of the proposed approach are proved for which numerical results are also reported.