This school is oriented to the presentation of theory, algorithms and applications for the solution of Mixed Integer Non-linear Problems (MINLP). This type of problems appears in numerous application areas where the modelization of non-linear phenomena with logical constraints is important; we must remember here the memorable phrase “the world is non-linear”.

Nowadays the theoretical aspects of this area are spread in a number of recent papers which makes it difficult, for non-specialist, to have a solid background of the existing results and new advances in the field. This school aims to present and develop this material in a organized way . Moreover, it also pursues to link theory with actual applications. In particular, remarkable applications can be found in air traffic control agencies, the air companies, the electric power generation companies, the chemical complex units, the analysis of financial products usually associated with risk dealing and in the algorithms in the statistical field and artificial intelligence as for instance artificial neural networks, or supporting vector machines, among many others.

The course will be taught by two leading experts in the area: Jeff Linderoth (University of Wisconsin) and Robert Weinsmantel (ETH, Zurich).

This school is addressed to PhD students and young researchers who wish to gain expertise in this field. MSRI and the local organizers will select a number of candidates (between 30-35) that will be financially supported to attend the school. MSRI will funds 10 students enrolled in US universities. IMUS will fund another 15 students and junior researchers coming from Spain, North Africa, and other European Countries.

This school will be included within the panel of courses offered to PhD students of the “Programa de Doctorado Matemáticas de la US” for the academic year 2015-16 and also offered to other PhD programs in Mathematics in Spain. Therefore, it will be eligible to be recorded in the “Documento de Actividades del doctorando”. We expect to attract a good number of PhD students from different research areas.

School Organization

The school will present, in a unified way, the current theory together with the more recent algorithms designed to address some families of problems; we will also introduce the participants to the usage of specific solvers devoted to formulate and solve instances of these problems. The lecturers will start with basic concepts, in order to be interesting for beginners, to eventually discuss advanced topics of this emerging area of mathematical optimization.

The program activities will be: Two lectures taught in the mornings and organized in two sessions with a break in between.

  1. Lectures:
    1. The Theory of Mixed Integer Non-linear Programming.
    2. Modeling aspects and applications of Mixed Integer Non-linear programming.
  2. Problem solving and applications sessions will be organized during the afternoon, and led by the TAs. These sessions will be devoted to working on problem sets, on real life applications, and on various projects developed by the students. Lab sessions with available MINLP solvers will also be included.
  3. A cornerstone of the program is having students’ presentations about basic topics in the field. This allows students, even those with a more limited background, to work with source materials, and to practice lecturing about what they learn. We will ask students to prepare short (25-30 minute) talks on research papers of their choice. We will guide them in the preparation of their talk, as well as provide constructive criticisms of their presentation.

Organizing Comittee

  • Francisco Castro Jiménez. (Universidad de Sevilla)
  • Elena Fernández. (Universitat Politècnica de Catalunya)
  • Justo Puerto Albandoz. (Universidad de Sevilla and member of IMUS)


IMUS (Institute of Mathematics of the University of Seville)

MSRI (Mathematical Sciences Research Institute)

EURO (Association of European Operational Research Societies)