Delayed Weighted Gradient Method with simultaneous step-sizes for strongly convex optimization

The Delayed Weighted Gradient Method (DWGM) is a two-step gradient algorithm that is efficient for the minimization of large scale strictly convex quadratic functions. It has orthogonality properties that make it to compete with the Conjugate Gradient (CG) method. Both methods calculate in sequence two step-sizes, CG minimizes the objective function and DWGM the gradient norm, alongside two search directions defined over first order current and previous iteration information. The objective of this work is to accelerate the recently developed extension of DWGM to nonquadratic strongly convex minimization problems. Our idea is to define the step-sizes of DWGM in a unique two dimensional convex quadratic optimization problem, calculating them simultaneously. Convergence of the resulting algorithm is analyzed. Comparative numerical experiments illustrate the effectiveness of our approach.