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
University of Michigan
Ann Arbor, MI 48109-2117
USA
**********************************************************
*
* Contributions to be spread via DMANET are submitted to
*
* DMANET@zpr.uni-koeln.de
*
* Replies to a message carried on DMANET should NOT be
* addressed to DMANET but to the original sender. The
* original sender, however, is invited to prepare an
* update of the replies received and to communicate it
* via DMANET.
*
* DISCRETE MATHEMATICS AND ALGORITHMS NETWORK (DMANET)
* http://www.zaik.uni-koeln.de/AFS/publications/dmanet/
*
**********************************************************
Posts
