On the choice of step size in subgradient optimization

This paper recommends some procedures for the selection of step sizes in the context of subgradient optimization. The first of these procedures is developed in detail in this study and is a theoretically convergent scheme. This method has two phases, the first phase is designed to accelerate the solution procedure towards an optimal solution, while the second phase helps to close in on an optimal solution. A second technique recommended is a simple-minded scheme which, although not theoretically convergent, seems to be computationally very efficient. These two methods are shown to compare favorably with Held, Wolfe and Crowder's scheme for prescribing step sizes. We also suggest some modifications of the latter scheme to make it computationally more efficient.