Improving a gradient based algorithm using the momentum term

Abstract

There are a number of algorithms that can be categorized as gradient based. One such algorithm is the Dynamic Integrated Systems Optimization and Parameter Estimation algorithm meant for solving nonlinear optimal control problems. A common trait to gradient based algorithms is that their search direction is determined by the gradient vector of the objective function. One peculiar behavior of gradient based searches is that any two consecutive directions would be perpendicular to each other. Because of this, the path of the search will zigzag towards the optimal solution. The zigzag movement of the search is associated with the unfavorable e?ect of slowing down the algorithms especially when the surface of the function is in the form of ravines. This chapter proposed the use of momentum term to append the search mechanism of said algorithm in order to overcome this zigzag problem. In our simulation we found that the momentum term managed to decrease the number of iterations needed by this algorithm to arrive at the optimum