The Descent–Ascent Algorithm for DC Programming

We introduce a bundle method for the unconstrained minimization of non smooth difference-of-convex (DC) functions, and it is based on the calculation of a special type of descent direction called descent-ascent direction. The algorithm only requires evaluations of the minuend component function at each iterate, and it can be considered as a parsimonious bundle method as accumulation of information takes place only in case the descent-ascent direction does not provide a sufficient decrease. No line search is performed, and proximity control is pursued independent of whether the decrease in the objective function is achieved. Termination of the algorithm at a point satisfying a weak criticality condition is proved, and numerical results on a set of benchmark DC problems are reported.