Institut für Numerische und Angewandte Mathematik A general solution algorithm for non-convex mixed integer optimization problems with only few continuous variables

Geometric branch-and-bound techniques are well-known solution algorithms for non-convex global optimization problems. Several approaches can be found in the literature differing mainly in the bounds used. The aim of this paper is to extend geometric branch-and-bound methods to mixed integer optimization problems, i.e. to objective functions with some continuous and some integer variables. We derive several bounding operations and analyze their rates of convergence theoretically. Moreover we show that the accuracy of any algorithm for solving the problem with fixed integer variables can be transferred to the mixed integer case. Our results are demonstrated theoretically and experimentally using the truncated Weber problem and the multisource Weber problem. For both problems we succeed in finding exact optimal solutions.