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

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.