A new black box method for monotone nonlinear equations. (4th May 2023)

• Record Type: Journal Article
• Authors: Ibrahim, Abdulkarim Hassan; Kimiaei, Morteza; Kumam, Poom
• Is Part Of: Optimization. Volume 72:Number 5(2023)
• Page Start: 1119
• Page End: 1137
• Publication Date: 2023-05-04
• Subjects: Nonlinear monotone equations -- derivative-free optimization -- line search method -- global convergence; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2021.2002326
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract : This paper discusses a new derivative-free line search method for nonlinear monotone equations. It uses a derivative-free direction based on Dai–Liao method, along which an improved line search – called IDFLS – is tried. In contrast to the basic line search method – called BasicLS – by Solodov and Svaiter, IDFLS uses extrapolation steps to guarantee a decrease in the function norm. In fact, IDFLS never accept a point with the worst function norm, while BasicLS may accept such a point. The global convergence of our method is established under the assumption that the underlying mapping is monotone. The numerical results show that the new method is competitive in comparison with the state-of-the-art methods.