An Accelerated Spectral Perry-Type Conjugate Gradient Projection Method for Unconstrained Nonlinear Equations with Applications

In this paper, we propose an accelerated spectral Perry-type conjugate gradient projection method for solving systems of unconstrained nonlinear equations. The spectral parameter is generated using an accelerated gradient-descent method, which ensures that the proposed search direction always satisfies the sufficient descent condition. By incorporating a self-adaptive strategy into the optimal Perry conjugate parameter, the proposed search direction possesses the trust region property independent of any line search. Additionally, the proposed method incorporates an inertial extrapolation step to enhance computational performance. The global convergence of the proposed method is theoretically established without requiring monotonicity or pseudo-monotonicity of the underlying mapping. Numerical experiments on systems of unconstrained nonlinear equations and image de-blurring problems demonstrate the effectiveness of the proposed method.