A Transformation of Accelerated Double Step Size Method for Unconstrained Optimization

Abstract

A reduction of the originally double step size iteration into the single step length scheme is derived under the proposed condition that relates two step lengths in the accelerated double step size gradient descent scheme. The proposed transformation is numerically tested. Obtained results confirm the substantial progress in comparison with the single step size accelerated gradient descent method defined in a classical way regarding all analyzed characteristics: number of iterations, CPU time, and number of function evaluations. Linear convergence of derived method has been proved.