An inertial Fletcher-Reeves-type conjugate gradient projection-based method and its spectral extension for constrained nonlinear equations

In this paper, we initially enhance the Fletcher-Reeves (FR) conjugate parameter through a shrinkage multiplier, leading to a derivative-free two-term search direction and its extended spectral version. The results indicate that both search directions demonstrate sufficient descent and trust-region properties, irrespective of the line search method utilized. Then, by combining the hyperplane projection-based approach and inertia technique, we present two inertial FR-type conjugate gradient projection-based methods for solving constrained nonlinear equations. The global convergence of our methods is theoretically established, without requiring the monotonicity or pseudo-monotonicity of the underlying mapping, nor the Lipschitz continuity condition. Numerical experiments conducted on constrained nonlinear equations, as well as applications in regularized decentralized logistic regression problems and sparse signal restoration problems, have demonstrated the numerical efficacy of our methods.