A derivative-free three-term projection algorithm involving spectral quotient for solving nonlinear monotone equations

作者：Gao Peiting; He Chuanjiang^*

来源：Optimization, 2018, 67(10): 1631-1648.

DOI：10.1080/02331934.2018.1482490

• Nonlinear monotone equations
• projection method
• spectral quotient
• global convergence

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].

• 出版日期2018
• 单位重庆大学