Variations and extension of the convex–concave procedure

We investigate the convex–concave procedure, a local heuristic that utilizes the tools of convex optimization to find local optima of difference of convex (DC) programming problems. The class of DC problems includes many difficult problems such as the traveling salesman problem. We extend the standard procedure in two major ways and describe several variations. First, we allow for the algorithm to be initialized without a feasible point. Second, we generalize the algorithm to include vector inequalities. We then present several examples to demonstrate these algorithms.