A derivative-free three-term projection algorithm involving spectral quotient for solving nonlinear monotone equations. (3rd October 2018)

• Record Type: Journal Article
• Authors: Peiting, Gao; Chuanjiang, He
• Is Part Of: Optimization. Volume 67:Number 10(2018)
• Page Start: 1631
• Page End: 1648
• Publication Date: 2018-10-03
• Subjects: Nonlinear monotone equations -- projection method -- spectral quotient -- global convergence; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2018.1482490
• Languages: English
• ISSNs: 0233-1934

Abstract

ABSTRACT: In this paper, we develop a three-term conjugate gradient method involving spectral quotient, which always satisfies the famous Dai-Liao conjugacy condition and quasi-Newton secant equation, independently of any line search. This new three-term conjugate gradient method can be regarded as a variant of the memoryless Broyden-Fletcher-Goldfarb-Shanno quasi-Newton method with regard to spectral quotient. By combining this method with the projection technique proposed by Solodov and Svaiter in 1998, we establish a derivative-free three-term projection algorithm for dealing with large-scale nonlinear monotone system of equations. We prove the global convergence of the algorithm and obtain the R-linear convergence rate under some mild conditions. Numerical results show that our projection algorithm is effective and robust, and is more competitive with the TTDFP algorithm proposed Liu and Li [A three-term derivative-free projection method for nonlinear monotone system of equations. Calcolo. 2016;53:427–450].