The q-gradient method used a Yuan step size for odd steps, and geometric recursion as an even (q-GY). This study aimed to accelerate convergence minimum point by minimizing the number of iterations, dilating parameter q independent variable then comparing results with three algorithms namely, classical steepest descent (SD) method, Steps (SDY), (q-G). numerical were presented in tables graphs. ...

This paper describes a hybrid steepest descent method to decrease over time any given convex cost function while keeping the optimization variables into any given convex set. The method takes advantage of properties of hybrid systems to avoid the computation of projections or of a dual optimum. The convergence to a global optimum is analyzed using Lyapunov stability arguments. A discretized imp...

We consider the special case of the restarted Arnoldi method for approximating the product of a function of a Hermitian matrix with a vector which results when the restart length is set to one. When applied to the solution of a linear system of equations, this approach coincides with the method of steepest descent. We show that the method is equivalent to an interpolation process in which the n...

The negative gradient direction to find local minimizers has been associated with the classical steepest descent method which behaves poorly except for very well conditioned problems. We stress out that the poor behavior of the steepest descent methods is due to the optimal Cauchy choice of steplength and not to the choice of the search direction. We discuss over and under relaxation of the opt...