Piece adding technique for convex maximization problems

In this article we provide an algorithm, where to escape from a local maximum y of convex function f over D, we (locally) solve piecewise convex maximization max{min{f (x) − f (y), p _y (x)} | x ∈ D} with an additional convex function p _y (·). The last problem can be seen as a strictly convex improvement of the standard cutting plane technique for convex maximization. We report some computational results, that show the algorithm efficiency.