On the new spectral conjugate gradient‐type method for monotone nonlinear equations and signal recovery

We present a new approach for constructing a spectral conjugate gradient‐type method for solving nonlinear equations. The proposed method uses an approximate optimal step size together with the memoryless Broyden–Fletcher–Goldfarb–Shanno (BFGS) formula to generate a new choice of the spectral conjugate gradient‐type direction that satisfies the sufficient descent condition without line search requirement. The global convergence of the method is achieved under some mild assumptions. Numerical experiments on both nonlinear monotone equations and signal reconstruction problems reveal the efficiency of the new approach.