This work addresses the development of an efficient solution strategy for obtaining global optima of continuous, integer, and mixed-integer nonlinear programs. Towards this end, we develop novel relaxation schemes, range reduction tests, and branching strategies which we incorporate into the prototypical branch-and-bound algorithm. In the theoretical/algorithmic part of the paper, we begin by d...

an interactive heuristic approach can offer a practical solution to the problem of linear integer programming (lip) by combining an optimization technique with the decision maker’s (dm) judgment and technical supervision. this is made possible using the concept of bicriterion linear programming (blp) problem in an integer environment. this model proposes two bicriterion linear programs for iden...

The Discrete Ordered Median Problem (DOMP) generalizes classical discrete location problems, such as the N -median, N -center and Uncapacitated Facility Location problems. It was introduced by Nickel [16], who formulated it as both a nonlinear and a linear integer program. We propose an alternative integer linear programming formulation for the DOMP, discuss relationships between both integer l...

We discuss a mixed-integer nonlinear programming formulation for the problem of covering a set of points with a given number of slabs of minimum width, known as the bottleneck variant of the hyperplane clustering problem. We derive several linear approximations, which we solve using a standard mixed-integer linear programming solver. A computational comparison of the performance of the differen...

We overview our recently introduced theory of n-fold integer programming which enables the polynomial time solution of fundamental linear and nonlinear integer programming problems in variable dimension. We demonstrate its power by obtaining the first polynomial time algorithms in several application areas including multicommodity flows and privacy in statistical databases.