A revised Liu–Storey conjugate gradient parameter for unconstrained optimization problems with applications

ABSTRACT

Conjugate Gradient (CG) methods are renowned for their efficiency and low memory requirements when solving optimization problems. However, certain formulations of CG methods that switch between two or more CG parameters often overlook specific values that could have been integrated. Moreover, the demonstration of the sufficient descent property in these methods usually relies on a strategy that assumes the possible exclusion of certain function values. To alleviate this assumption, this article introduces a structured Liu–Storey spectral CG method. This method extends the formulation of the spectral Fletcher conjugate descent method, enabling it to maintain fast convergence and inherit a good restart property. Therefore, the method ensures that the sufficient descent property holds without additional requirements and converges globally via some standard assumptions. Additionally, the method proves useful in solving robotic and image reconstruction models. Finally, it demonstrates robustness when compared to some standard algorithms.

KEYWORDS:

• Unconstrained optimization
• spectral conjugate gradient method
• sufficient descent criteria
• motion control
• image recovery

Disclosure statement

The authors declare they have no competing interests.

Data availability statement

All the necessary data are included in the manuscript.

Additional information

Funding

The authors acknowledge the support of the National Research Council of Thailand (NRCT) under the Research Grants for Talented Mid-Career Researchers [Contract No. N41A640089]; Nasiru Salihu also acknowledges the support of the Petchra Pra Jom Klao Doctoral Research Scholarship from King Mongkut's University of Technology Thonburi [Contract No. 52/2564] and the Center of Excellence in Theoretical and Computational Science (TaCS-CoE), KMUTT.