A nonmonotone scaled conjugate gradient algorithm for large-scale unconstrained optimization

ABSTRACT

This paper proposes a nonmonotone scaled conjugate gradient algorithm for solving large-scale unconstrained optimization problems, which combines the idea of scaled memoryless Broyden–Fletcher–Goldfarb–Shanno preconditioned conjugate gradient method with the nonmonotone technique. An attractive property of the proposed method is that the search direction always provides sufficient descent step at each iteration. This property is independent of the line search used. Under appropriate assumptions, the method is proven to possess global convergence for nonconvex smooth functions, and R-linear convergence for strongly convex functions. Preliminary numerical results and related comparisons show the efficiency of the proposed method in practical computation.

KEYWORDS:

• Unconstrained optimization
• nonmonotone line search
• scaled conjugate gradient algorithm
• convergence analysis
• numerical comparisons

MATHEMATICS SUBJECT CLASSIFICATION (2000):

• 90C30
• 65K05
• 49M37

Acknowledgments

The authors would like to thank the anonymous referees and the editor for their patience and valuable comments and suggestions that greatly improved this paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was partially supported by NNSF of China (Nos.11261015, 61762032) and NSF of Hainan Province (Nos. 2016CXTD004, 111001, 117014).