The 23rd edition of the Belgian Mathematical Optimization Workshop took place on the **25th and 26th of April 2019**. It was held at the Floréal Club, avenue de Villez, 6, 6980 La-Roche-en-Ardennes.

The invited speakers for this edition were Silvano Martello (DEI "Guglielmo Marconi", University of Bologna, Italy) and Claudia D'Ambrosio (LIX, École Polytechnique, Palaiseau, France).

This year's edition was supported by ORBEL.

### Invited speakers

#### Thursday, April 25, 10:30-12:30

**Silvano Martello**

*DEI “Guglielmo Marconi”, Alma Mater Studiorum Università di Bologna*

*Bin packing problems*

Slides

The tutorial will present an overview of models and algorithms for the one-dimensional bin
packing problem. This is one of the most famous strongly NP-hard problems in combina-
torial optimization. Its structure and its applications have been studied since the Thirties
(Kantorovich). In the early Sixties Gilmore and Gomory introduced, for this class of prob-
lems, the concept of column generation. This is one of the first problems for which, since the
early Seventies, the worst-case performance of approximation algorithms was investigated.
In the Eighties and Nineties lower bounds were studied and effective exact algorithms were
developed. In the following years many heuristic and metaheuristic approaches have been
introduced. In the 2000s, branch(-and-cut)-and-price algorithms and pseudo-polynomial
formulations have been successfully used for its exact solution. Extensions to the two- and
three-dimensional case will also be reviewed.

#### Friday, April 26, 10:30-12:30

**Claudia D'Ambrosio**

*LIX, École Polytechnique, Palaiseau, France*

*Mixed Integer Non Linear Programming*

Slides

In this tutorial we aim at surveying on the fundamentals of theoretical and practical aspects of mixed integer non linear programming (MINLP). MINLPs are very powerful and challenging optimization problems that can represent an extremely large variety of real-world applications. The first part of the tutorial will be devoted to an introduction to MINLP in general and on algorithm for nonconvex MINLPs. In the second part, we will consider some well-structured classes of nonconvex MINLPs and introduce tailored methods solve them.

**Contact: **Bernard Fortz