Partially symmetrical derivative-free Liu–Storey projection method for convex constrained equations

ABSTRACT

Applying Powell symmetrical technique to the Liu–Storey conjugate gradient method, a partially symmetrical Liu–Storey conjugate gradient method is proposed and extended to solve nonlinear monotone equations with convex constraints, which satisfies the sufficient descent condition without any line search. By using some line searches, the global convergence is proved merely by assuming that the equations are Lipschitz continuous. Moreover, we prove the R-linear convergence rate of the proposed method with an additional assumption. Finally, compared with one existing method, the performance of the proposed method is showed by some numerical experiments on the given test problems.

KEYWORDS:

• Nonlinear monotone equations
• conjugate gradient method
• symmetrical technique
• projection technique
• global convergence

SUBJECT CLASSIFICATION MSC (2010):

• 90C30
• 65K05

Acknowledgments

The authors wish to express their heartfelt thanks to the referees for their detailed and helpful suggestions for revising the manuscript.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by Chongqing Research Programme of Basic Research and Frontier Technology [grant number cstc2017jcyjAX0318], Programme for Innovation TeamBuilding at Institutions of Higher Education in Chongqing [grant number CXTDX201601035], Chongqing Municipal Key Laboratory of Institutions of Higher Education [grant number [2017]3], and the fund of Scientific and Technological Research Programme of Chongqing Municipal Education Commission [grant number KJQN201801208].