[ Français ]

The next seminar will be held on October 22 at Pavillon André Aisenstadt, room 5340, 4:30 PM
Dr. Jean-Bernard Lasserre (CNRS, France) - Connecting optimization with spectral analysis of tri-diagonal Hankel matrices


Mixed-integer nonlinear programming (MINLP) is concerned with finding optimal solutions to mathematical-optimization models that combine both discrete and (continuous) nonlinear elements. Models with this flavor arise in important applications in many domains, notably chemical engineering, energy, and transportation. Moreover, the well-developed frameworks for discrete and continuous optimization are not sufficient in themselves to attack this broad class of models. The underlying mathematical complexity is not as well understood due to the combination of how non-convexities arise from both the discrete and nonlinear elements. In particular, there remain theoretical, algorithmic and computational challenges before MINLP can enjoy a success similar to, say, smooth optimization or integer linear programming. These research challenges, together with the potential for remarkable impact, make MINLP arguably the most exciting new frontier in mathematical optimization. MINLP has caught the attention of all major optimization societies which have fostered work in this area. MINLP has also established new and significant links between industry and academia.

The thematic activity hosted by the Centre de Recherche Mathématiques of Montréal will feature visits for the entire month of six distinguished researchers:

  • Amitabh Basu (Johns Hopkins U, USA)
  • Claudia D'Ambrosio (CNRS, France)
  • Marcia Fampa (Universidade Federal do Rio de Janeiro, Brasil)
  • Jean-Bernard Lasserre (CNRS, France)
  • Jon Lee (U Michigan, USA)
  • Ruth Misener (Imperial College, UK)

They will animate a regular series of seminars and tutorial sessions.

In addition to that series, the activity will feature a workshop organized and funded in cooperation with DIMACS to be held on October 7-10, 2019. Most oral presentations of the workshop will be given by invited speakers. Confirmed speakers are:

  • Amir Ali Ahmadi
  • Dan Bienstock
  • Christoph Buchheim
  • Santanu Dey
  • Aida Khajavirad
  • Leo Liberti
  • Jeff Linderoth
  • Sebastian Sager
  • Nick Sahinidis
  • Renata Sotirov
  • Mohit Tawarmalani
  • Juan Pablo Vielma
  • Robert Weismantel

In addition to oral presentations, a poster session will showcase recent developments by both academic and industrial participants. Authors interested in contributing papers to the workshop, please email by clicking on this link by August 15, 2019.

Contributed papers will be included mostly in the poster session, although opportunities for oral presentations may arise.

Limited support to students for attending the workshop might be provided. Interested students should apply by email by clicking on this link by September 1, 2019, with a supporting letter from their supervisor.

Venue: Université de Montréal Campus

Registration: Early registration fee $75 CAD by August 15
Late registration fee 125 CAD by September 15
Montreal-based students will be treated in a separate way, please send an email by clicking on this link by September 15. Other activities

André Aisenstadt, room 5340
October 15, 4:30 PM
Gabriele Iommazzo (Polytechnique, France)

Algorithmic Configuration By Learning And Optimization

I will present a methodology, based on machine learning and mathematical optimization, for selecting a solver configuration for a given instance. The approach first employs a set of solved instances and configurations in order to learn a performance function of the solver. Secondly, it solves a mixed-integer nonlinear program in order to find the best algorithmic configuration based on the learned performance function.

André Aisenstadt, room 5340
October 17, 11:30 AM
Dr. Amitabh Basu (Johns Hopkins, USA)
Centerpoints: A link between optimization and convex geometry

We introduce a concept that generalizes several different notions of “centerpoint” in the literature. We develop an oracle based algorithm for convex (nonlinear) mixed-integer optimization based on this idea of centerpoints. We show that algorithms based on centerpoints are “best possible” in a certain precise sense. Motivated by this, we establish several structural results around this concept and provide efficient algorithms for computing these points. Pur main motivation is to understand the complexity of oracle based convex mixed-integer optimization.

André Aisenstadt, room 5340
Octobre 22, 4:30 PM
Dr. Jean-Bernard Lasserre (CNRS, France)
Connecting optimization with spectral analysis of tri-diagonal Hankel matrices

We show that the global minimum (resp. maximum) of a continuous function on a compact set can be approximated from above (resp. from below) by computing the smallest (rest. largest) eigenvalue of a hierarchy of (r x r) tri-diagonal Hankel matrix of increasing size. Equivalently it reduces to computing the smallest (resp. largest) root of a certain univariate degree-r orthonormal polynomial. This provides a strong connection between the fields of optimization, orthogonal poly-nomials, numerical analysis and linear algebra, via asymptotic spectral analysis of tri-diagonal Hankel matrices.