On Poljak's improved subgradient method

Poljak has suggested an improved subgradient method and provided a lower bound on the improvement of the Euclidean distance to an optimal solution. In this paper, we provide a stronger lower bound and show that the direction of movement in this method forms a more acute angle with the direction toward the set of optimal solutions than that in the subgradient method.Most of this research has been performed while the first author was visiting the Decision and Information Systems Department, College of Business, Arizona State University, Tempe, Arizona.