Piece adding technique for convex maximization problems

摘要

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.