Wei–Yao–Liu conjugate gradient projection algorithm for nonlinear monotone equations with convex constraints

Abstract

In this paper, the Wei–Yao–Liu (WYL) conjugate gradient projection algorithm will be studied for nonlinear monotone equations with convex constraints, which can be viewed as an extension of the WYL conjugate gradient method for solving unconstrained optimization problems. These methods can be applied to solving large-scale nonlinear equations due to the low storage requirement. We can obtain global convergence of our algorithm without requiring differentiability in the case that the equation is Lipschitz continuous. The numerical results show that the new algorithm is efficient.

Keywords:

• nonlinear monotone equations
• large-scale
• Wei–Yao–Liu conjugate gradient algorithm
• projection method
• global convergence

AMS 2000 Subject Classifications:

• 90C25
• 90C30

Acknowledgements

The authors would appreciate the great work of the referees for their valuable comments and suggestions which would be sure to lead to significant improvements in this paper. This work was supported by the National Natural Science Foundation of China (No. 11161003 11261006) and the Guangxi Natural Science Foundation (No. 2012GXNSFAA053002).