A new subspace minimization conjugate gradient method based on tensor model for unconstrained optimization

ABSTRACT

A new subspace minimization conjugate gradient method based on tensor model is proposed and analysed. If the objective function is close to a quadratic, we construct a quadratic approximation model in a two-dimensional subspace to generate the search direction; otherwise, we construct a tensor model. It is remarkable that the search direction satisfies the sufficient descent property. We prove the global convergence of the proposed method under mild assumptions. Numerical comparisons are given with well-known CGOPT and CG_DESCENT and show that the proposed algorithm is very promising.

KEYWORDS:

• Conjugate gradient method
• tensor model
• subspace technique
• non-monotone line search
• unconstrained optimizaiton

2010 MATHEMATICS SUBJECT CLASSIFICATIONS:

• 90C30
• 90C06
• 65K05

Acknowledgements

The author would like to thank Professor Y.H. Dai and Dr C.X. Kou for their CGOPT code, and thank Professors W.W. Hager and H. Zhang for their CG_DESCENT (5.3) code.

Disclosure statement

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

Additional information

Funding

This research is supported by National Natural Science Foundation of China (grant number 11461021), Guangxi Science Foundation (grant number 2017GXNSFBA198031) and Shaanxi Science Foundation (grant number 2017JM1014).