Abstract:

As a generalization of the two-term conjugate gradient method (CGM), the spectral CGM is one of the effective methods for solving unconstrained optimization. In this paper, we enhance the JJSL conjugate parameter, initially proposed by Jiang et al. (Computational and Applied Mathematics, 2021, 40: 174), through the utilization of a convex combination technique.

And this improvement allows for an adaptive search direction by integrating a newly constructed spectral gradient-type restart strategy. Then, we develop a new spectral CGM by employing an inexact line search to determine the step size. With the application of the weak Wolfe line search, we establish the sufficient descent property of the proposed search direction. Moreover, under general assumptions, including the employment of the strong Wolfe line search for step size calculation, we demonstrate the global convergence of our new algorithm. Finally, the given unconstrained optimization test results show that the new algorithm is effective.

Key words: Unconstrained optimization, Spectral conjugate gradient method, Restart strategy, Inexact line search, Global convergence