« CRM/DIMACS Workshop on Mixed-Integer Nonlinear Programming
October 07, 2019 - October 10, 2019
Auditorium (Amphitheatre Banque Nationale)
Click here for map.
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.
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)
Monday, October 7, 2019
Welcome and Opening Remarks
Modeling Power of Mixed Integer Convex Optimization Problems And Their Effective Solution with Julia and JuMP
Juan Pablo Vielma, Massachusetts Institute of Technology
New Relaxations for Composite Functions
Mohit Tawarmalani, Purdue University
On Solving Mixed Integer Non Linear Programs with Separable Non Convexities
Claudia D’Ambrosio, CNRS and Ecole Polytechnique
Spectral Relaxations and Branching Strategies for Global Optimization of Mixed-integer Quadratic Programs
Nick Sahinidis, Carnegie Mellon University
Sparse Cutting Planes For Quadratically-Constrained Quadratic Programs
Aleksandr Kazachkov, Polytechnique Montréal
Random Projections for Quadratic Programming
Leo Liberti, CNRS and Ecole Polytechnique
Poster Session and Reception
Tuesday, October 8, 2019
Integer Optimization from the Perspective of Determinants
Robert Weismantel, ETH Zurich
On Local Minima of Cubic Polynomials
Amir Ali Ahmadi, Princeton University
Mixed-Integer Convex Nonlinear Optimization with Gradient-Boosted Trees Embedded
Ruth Misener, Imperial College London
Perspectives on Integer Programming in Sparse Optimization
Jeff Linderoth, University of Wisconsin, Madison
Some Ideas for the Simplex Method on a Quantum Computer
Giacomo Nannicini, IBM Research
Linear Programming for Community Detection and Data Clustering
Aida Khajavirad, Rutgers University
Wednesday, October 9, 2019
Linearization Based Bounds for Binary Quadratic Problems
Renata Sotirov, Tilburg University
Convexification and Linearization in MINLP
Marcia Fampa, Federal University of Rio de Janeiro
Jean-Bernard Lasserre, French National Centre for Scientific Research
On Sufficient and Necessary Conditions for Rank-1 Generatedness Property of Cones
Fatma Kılınç-Karzan, Carnegie Mellon University
Implementing a Smooth Exact Penalty Function for Nonlinear Optimization
Dominique Orban, GERAD and Ecole Polytechnique
Thursday, October 10, 2019
Jon Lee, University of Michigan
Oracle-based Algorithms for Robust Combinatorial Optimization
Christoph Buchheim, Technical University of Dortmund
Mixed-integer Conic Optimization: Strong Subadditive Duals and Extended Formulations
Akshay Gupte, Clemson University
Complexity of Branch-and-bound and Cutting Plane Algorithms
Amitabh Basu, Johns Hopkins University
Convexification of Substructures in Quadratically Constrained Quadratic Program
Santanu Dey, Georgia Institute of Technology
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.
Sponsored by Centre de Recherches Mathématiques, in association with the Special Focus on Bridging Continuous and Discrete Optimization.
Please click here to get information for travel and accomodations information for this event.