An accelerated relaxed-inertial strategy based CGP algorithm with restart technique for constrained nonlinear pseudo-monotone equations to image de-blurring problems

Abstract

In this paper, an accelerated spectral conjugate gradient projection algorithm is proposed for solving the constrained nonlinear pseudo-monotone equations. We set a restart procedure related to the conjugate parameter in the search direction of the spectral conjugate gradient method. We use an accelerated gradient descent scheme to generate the spectral parameter. Finally, we adopt the relaxed-inertial strategy to accelerated algorithm iteration process. Global convergence is proved under mild conditions without the Lipschitz continuity assumption. Numerical comparisons with other methods show the performances of our algorithm for solving large-scale equations. Our applications are on regularized decentralized logistic regression and image de-blurring problems.