An amazing variety of activities and situations can be adequately modeled as linear optimization problems, also known as linear programs (LPs), or convex nonlinear optimization problems. Adequately means that the degree of approximation to reality that such a representation involves is acceptable. However, as the world that we inhabit is neither linear nor convex, the most common obstacle to th...

This manuscript introduces ANTIGONE, Algorithms for coNTinuous / Integer Global Optimization of Nonlinear Equations, a general mixed-integer nonlinear global optimization framework. ANTIGONE is the evolution of the Global Mixed-Integer Quadratic Optimizer, GloMIQO, to general nonconvex terms. The purpose of this paper is to show how the extensible structure of ANTIGONE realizes our previously-p...

• Lattices. We will see basic properties of lattices, followed by Minkowski’s Theorem which guarantees that any symmetric convex set with volume bigger than 2 must have an non-zero integer point. We will show an application of Minkowski’s theorem to Diophantine approximations. Then we will introduce the powerful concept of Lattice basis reduction which finds an almost orthogonal basis for a lat...

Performance aspects of a Lagrangian relaxation based heuris-tic for solving large 0-1 integer linear programs are discussed. In particular , we look at its application to airline and railway crew scheduling problems. We present a scalable parallelization of the original algorithm used in production at Carmen Systems AB, GG oteborg, Sweden, based on distributing the variables and a new sequentia...