Spring School

ISCO 2018 will be preceded by a spring school on

“Advanced Mixed Integer Programming Formulation Techniques”

Lecturers

 from Massachusetts Institute of Technology (MIT), USA.

They will give 16 hours of lectures.

The Spring School will be organized before the conference, on April 9-10 in the same venue. 

Abstract

Mixed-integer programming (MIP) extends standard continuous optimization by allowing us to impose that some of the decision variables must take integer values. A wide range of problems can be modeled as linear or convex MIPs whose continuous relaxation are either linear or convex optimization problems, respectively. There exist standard techniques for constructing MIP formulations; however, they may not yield an ideal balance among the various favorable formulation properties that can be crucial for good performance with state-of-the-art solvers. In this spring school we will cover both theoretical and practical aspects related to the construction of advanced MIP formulations that can favorably balance these desirable properties and can yield a significant computational advantage. Theoretical topics will include characterizations of the expressive power of MIP modeling, as well as and lower bounds on the sizes of formulations for unions of polyhedra. Practical topics will include specific formulation construction techniques and an overview of the Julia-based JuMP modeling language.

Program

 

April 9 (morning)

  • 8.30-10.30: Introduction to MIP formulations and their computationally favorable properties (Joey)
  • 11.00-13.00: Advanced geometric construction techniques for unions of polytopes (Juan Pablo)

 

April 9 (afternoon)

  • 14.30-16.30: Advanced combinatorial construction techniques for unions of polytopes (Joey)
  • 16.30-17.00: Coffee Break
  • 17.00-19.00: Characterizations of what can be modeled with linear and convex MIP (Juan Pablo)

 

April 10 (morning)

  • 8.30-10.30: Branch-and-bound and MIP formulations (Joey)
  • 11.00-13.00: Convex MIP formulation techniques (Juan Pablo)

 

April 10 (afternoon)

  • 14.30-16.30: Constructing and solving MIPs with the JuMP modeling language (Joey)
  • 16.30-17.00: Coffee Break
  • 17.00-19.00: Using linear MIP formulations to approximately solve nonlinear MIPs (Juan Pablo)