An inertial spectral conjugate gradient projection method for constrained nonlinear pseudo-monotone equations

Consider the nonlinear pseudo-monotone equations over a nonempty closed convex set. A spectral conjugate gradient projection method with the inertial factor is proposed for solving the problem under discussion. Following the projection strategy, we prove that the sequence of spectral parameters is bounded. The search direction generated by the algorithm satisfies the sufficient descent condition and possesses trust region property at each iteration. Under some mild conditions, the global convergence of the proposed method is established without the Lipschitz continuity assumption. Under some standard assumptions, we also establish the linear convergence rate of our method. Preliminary numerical results on constrained nonlinear monotone and pseudo-monotone equations demonstrate the efficiency of the proposed method. Furthermore, to highlight its applicability, we extend our method to deal with logistic regression problems.