Optimization in integers

Continuous linear or convex optimization problems are solved very efficiently. For example, continuous linear programs with tens, if not hundreds, of thousands of variables and constraints are commonly solved today. However, industrial applications very frequently impose integrity constraints on all or some of the variables; the resulting problems are generally much more difficult than their continuous versions. Progress made over the last twenty years has enabled us to efficiently solve many of these problems, often of considerable size, but we can still encounter problems with only a few hundred integer variables and constraints which cannot be solved exactly in a reasonable time, say in less than a few hours of computation. The present dossier provides an overview of the main theoretical and algorithmic tools available to tackle the exact solution of such problems, mentioning some of the most important applications.