An accelerated Dai–Yuan conjugate gradient projection method with the optimal choice

This article proposes an accelerated Dai–Yuan (DY) conjugate gradient (CG) projection method with the optimal choice for solving unconstrained pseudo-monotone nonlinear equations. Specifically, it first introduces a modified DY-type CG parameter with an indefinite factor and derives an optimal selection for this factor by minimizing the measure function. By combining the hyperplane projection approach, the inertial strategy, and a newly improved adaptive line search, the article presents an accelerated CG projection method. The proposed method is characterized by two main features: (i) the search direction is independent of any line search and possesses sufficient descent and trust region properties; and (ii) global convergence is achieved without requiring the underlying mapping to satisfy Lipschitz continuity. Additionally, the linear convergence rate of the method is proven under standard conditions. Numerical experiments on unconstrained nonlinear equations, as well as applications in signal restoration, demonstrate the effectiveness of the proposed method.