Concave minimization via conical partitions and polyhedral outer approximation

An algorithm is proposed for globally minimizing a concave function over a compact convex set. This algorithm combines typical branch-and-bound elements like partitioning, bounding and deletion with suitably introduced cuts in such a way that the computationally most expensive subroutines of previous methods are avoided. In each step, essentially only few linear programming problems have to be solved. Some preliminary computational results are reported.Parts of the present paper were accomplished while the author was on leave at the University of Florida.Parts of the present paper were completed while the author was on leave at the University of Trier as a fellow of the Alexander von Humboldt foundation.