[Opt-Net] CRM/DIMACS Workshop on Mixed-Integer Nonlinear Programming: October 7-10, 2019

[Jon Lee]

      CRM/DIMACS Workshop on Mixed-Integer Nonlinear Programming

October 07, 2019 - October 10, 2019

Location:

Université de Montréal Campus

Organizer(s):

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 simulatenously 
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 onMixed Integer Nonlinear Programming 
<http://www.crm.math.ca/crm50/en/category/mixed-integer-programming/>in 
October 2019 that is sponsored by theCentre de Recherches Mathématiques 
<http://www.crm.math.ca/crm50/en/>(CRM).

*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)

Juan Pablo Vielma (MIT)

Robert Weismantel (ETH Zürich)

Sponsored by Centre de Recherches Mathématiques and DIMACS, in 
association with theSpecial Focus on Bridging Continuous and Discrete 
Optimization <http://dimacs.rutgers.edu/programs/sf/sf-optimization/>.

Registration is required but not yet open.

http://dimacs.rutgers.edu/events/details?eID=%20321

-- 
Jon Lee
Industrial and Operations Engineering Department
1205 Beal Avenue
University of Michigan
Ann Arbor, MI 48109-2117
USA

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