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CRM/DIMACS Workshop on Mixed-Integer Nonlinear Programming

October 07, 2019 - October 10, 2019


Université de Montréal Campus


Andrea Lodi, Polytechnique Montréal

Bruce Shepherd, University of British Columbia

Mixed-Integer Nonlinear Programming (MINLP) is the study of optimization models which combine discrete and/or continuous variables with non-linear constraints and objectives.   As special cases, the fields of mixed-integer linear programming (MILP) and purely continuous convex or local nonlinear optimization (NLP) are relatively well-developed fields. The ambitious goal of MINLP is to work towards a fusion of the methods for discrete (MILP) and continuous (NLP), thereby extending the theoretical  advances and  broad applied impact enjoyed by  MILP and NLP.

Positive complexity results for MILP and NLP are well known. However, MINLP is a very broad modeling paradigm which, in its general form, produces undecidable computational questions. There have been, however, meaningful restrictions that have allowed some analysis in terms of exact and approximation algorithms. These include polynomial (quadratics in particular) objectives and constraints, (quasi-) convex function minimization, submodular function maximization, and reduced-dimensional functions. This very active line of research helps delineate the limits of what we can hope for from practical algorithms and software. Convexification techniques are playing an important role in this work, as it does in integer-linear optimization and global optimization for purely continuous optimization.  Other techniques are simultaneously being developed, including methods based on algebraic geometry and number theory.

Mixed-integer nonlinear programming is an attractive paradigm because it can naturally model the physics of a system (via continuous variables) and planning decisions (often via discrete variables). Because of demand from practitioners in many areas (but notably, chemical engineering, power-systems engineering, and operations research), there are many  sophisticated “general-purpose” software packages for mixed-integer nonlinear optimization. In addition, packages first conceived for mixed-integer linear programming now start to handle non-convex quadratic functions. Similarly, packages first conceived for (purely continuous) semi-definite programs and handling linear matrix inequalities are now emerging  to handle discrete variables. Work in mixed-integer nonlinear optimization has informed this growth and evolution in solvers, and this workshop aims to continue and accelerate the momentum in software growth.

There remain theoretical, algorithmic, and computational challenges to surmount before MINLP can enjoy a success that is comparable to MILP or NLP. These challenges, together with the potential for remarkable impact, make MINLP arguably the most exciting frontier in mathematical optimization.

The workshop will be held at Polytechnique Montréal in collaboration with a month-long program on Mixed Integer Nonlinear Programming in October 2019 that is sponsored by the Centre de Recherches Mathématiques (CRM). This flyer contains more information about the month-long program.

Advisory Committee:

Claudia D'Ambrosio (École Polytechnique, Paris), Marcia Fampa (Federal University of Rio de Janeiro), Fatma Kilinc-Karzan (Carnegie Mellon University), Jon Lee (University of Michigan)

Confirmed speakers include:

Amir Ali Ahmadi (Princeton University)

Dan Bienstock (Columbia University)

Christoph Buchheim (TU Dortmund)

Santanu Dey (Georgia Tech)

Aida Khajavirad (Rutgers University)

Leo Liberti (CNRS)

Jeff Linderoth (University of Wisconsin)

Sabastian Sager (Otto von Guericke University, Magdeburg)

Nick Sahinidis (Carnegie Mellon University)

Renata Sotirov (Tilburg University)

Mohit Tawarmalani (Purdue University)

Jaun Pablo Vielma (MIT)

Robert Weismantel (ETH Zürich)


The event is open to all who register. Most of the workshop presentations will be given by invited speakers.


In addition to oral presentations, a poster session will showcase recent developments by both academic and industrial participants. Authors interested in contributing abstracts for posters or presentations, please email the organizers with this link by August 15, 2019. Contributions will be included mostly in the poster session, although opportunities for oral presentations may arise.


Limited support to enable students to attend the workshop may be available.

Please note that early registration ends on August 15, 2019.