A globally convergent projection method for a system of nonlinear monotone equations

ABSTRACT

In this paper, a new conjugate gradient-based projection method for solving a system of nonlinear monotone equations is proposed. The method can be viewed as an extension of a family of conjugate gradient methods for unconstrained optimization by Li et al. [A new family of conjugate gradient methods for unconstrained optimization, J. Appl. Math. Comput. 58 (2018), pp. 219–234]. The proposed method is derivative-free which makes it suitable for large-scale nonlinear monotone equations. We show that the method satisfies the descent condition independent of line searches and that the method is globally convergent. Numerical results indicate that the proposed method is efficient.

KEYWORDS:

• Global convergence
• conjugate gradient
• projection method
• nonlinear monotone equations
• derivative-free

2010 AMS SUBJECT CLASSIFICATIONS:

• 90C06
• 90C56
• 65K05
• 65K10

Disclosure statement

No potential conflict of interest was reported by the author(s).