Two Novel Gradient Methods with Optimal Step Sizes (Journal of Computational Mathematics, 2021)
In this work we introduce two new Barzilai and Borwein-like steps sizes for the classical gradient method for strictly convex quadratic optimization problems. The proposedstep sizes employ second-order information in order to obtain faster gradient-type methods. Both step sizes are derived from two unconstrained optimization models that involveapproximate information of the Hessian of the objective function. A convergence analysis of the proposed algorithm is provided. Some numerical experiments are performedin order to compare the efficiency and effectiveness of the proposed methods with similarmethods in the literature. Experimentally, it is observed that our proposals accelerate thegradient method at nearly no extra computational cost, which makes our proposal a goodalternative to solve large-scale problems.