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.