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

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=%20321Posted on 2019-07-05 by*Sarah Fores*