An improvement of subgradient projection operator by composing monotonic functions

The subgradient projection operator has been utilized as a computationally efficient tool not only for suppression but also for minimization of convex functions in many applications. In this paper, we propose a systematic scheme to improve significantly the monotone approximation ability, of the subgradient projection, to the level set of a convex function. The proposed scheme is based on a simple observation: the level set of a convex function does not change by composing any zero-crossing monotonically increasing function. A numerical example demonstrates the effectiveness of the proposed scheme in an application to a simple boosting problem.