An Inertial Spectral Conjugate Gradient Method for Monotone Nonlinear Equations With Applications

This paper introduces an inertial spectral algorithm for solving monotone nonlinear equations, building upon prior developments in spectral methods for unconstrained optimization problems. Previous approaches introduced new spectral parameters and addressed such problems using a modified secant condition and quasi-Newton directions. We modify the search direction and integrates an inertial technique to improve numerical efficiency. The proposed method consistently ensures that the search direction satisfies the sufficient descent property independent of the method's line-search. We establish global convergence and a linear convergence rate under some standard assumptions. Extensive numerical experiments demonstrate the algorithm's strong performance, especially for large-scale problems. We also showcase its practical applications in logistic regression, a key model in data analysis, and sparse signal recovery, a prominent area in signal processing. The results emphasize the method's superior efficiency and effectiveness in these fields.