The DIMACS/Simons Collaboration on Bridging
Continuous and Discrete Optimization
[December, 2017] DIMACS is pleased to announce an
upcoming Special
Focus on Bridging Continuous and Discrete Optimization as part
of a broader partnership with the Simons Institute for the Theory
of Computing. The new DIMACS/Simons
Collaboration on Bridging Continuous and Discrete Optimization
features activities at both DIMACS and the Simons Institute that are
devoted to advancing capabilities in optimization by promoting
collaborations and methods that bridge continuous and discrete
optimization. The planned activities will bring together computer
scientists, mathematicians, operations researchers, engineers,
statisticians, and algorithm developers to advance both the
foundations and applications of optimization.
Optimization capabilities touch our everyday lives through more
efficient supply chains, better traffic management, more secure
power grids, and a host of other important applications. In the
short history of the field of mathematical optimization, advances in
underlying theory, practical implementation, and raw computing power
have brought us from solving linear programs with a few hundred
variables to those with more than a million. Widely available
general-purpose solvers make sophisticated tools for linear,
integer, and nonlinear programming broadly accessible to
practitioners. New applications, particularly those stemming from
machine learning and data science, are now challenging the field
with issues related to uncertainty, scale, speed, and complexity.
The field is responding with innovative approaches leading to
advances such as faster algorithms for maximum flow and
near-real-time approximations, more efficient interior-point
methods, and faster cutting-plane methods. Many of these innovations
bring together ideas from both continuous and discrete optimization.
Historically, continuous and discrete optimization have followed
largely distinct trajectories and drawn inspiration from different
branches of mathematics. The study of discrete optimization is most
closely associated with discrete mathematics and theoretical
computer science, while continuous optimization is rooted in the
well-developed mathematical theory of convex analysis and geometry.
Despite their different perspectives, the interplay between discrete
and continuous optimization has been and continues to be mutually
beneficial. In the last decade, partly stimulated by the growth of
machine learning and by the proliferation of massive datasets, new
areas of research have emerged at the interface of continuous and
discrete optimization and the flow between them is increasing. This
expanded interface has already led to a number of breakthroughs in
both areas, and the increasing pace of activity suggests that the
time is right to accelerate progress by stimulating collaboration
across the many communities of optimization. This is the goal of the
DIMACS/Simons Collaboration, which kicked off with an intensive Program
on Bridging Continuous and Discrete Optimization now underway
at the Simons Institute that will continue through the end of the
fall semester. Beginning with a Boot
Camp to introduce key themes, the Simons program brings
together roughly 120 faculty, postdocs, students, and researchers
from industry as long-term participants in the Simons program. The
Simons program also includes four workshops on: 1) Discrete
Optimization via Continuous Relaxation; 2) Fast
Iterative Methods in Optimization; 3) Hierarchies,
Extended Formulations and Matrix-Analytic Techniques; and 4) Optimization,
Statistics and Uncertainty.
In January 2018, the Collaboration continues with the launch of the
DIMACS
Special Focus on Bridging Continuous and Discrete Optimization,
which is scheduled to run through 2020. The DIMACS Special Focus
builds on the Simons program to involve a broader range of people
and institutions. It aims to advance the foundations and practical
applications of optimization via research visits, collaboration with
additional activities and institutes, and seven additional workshops
on the topics of:
• ADMM and Proximal Splitting Methods in
Optimization
• Optimization and Machine Learning
• Randomized Numerical Linear Algebra, Statistics,
and Optimization
• Continuous Approaches to Computing Discrete
Partition Functions
• Polynomial Optimization
• Optimization in Distance Geometry
• Mixed-Integer Nonlinear Optimization
Both DIMACS and the Simons Institute coordinate many of their
activities around designated scientific themes. Themed programs at
the Simons Institute typically span a single semester, while DIMACS
special foci typically span several years. The Collaboration on
Bridging Continuous and Discrete Optimization aims to leverage these
different timescales. The intense focus and energy of the Simons
program will launch the collaboration and build momentum around the
theme, while the longer time afforded by the DIMACS special focus
will allow ideas to broaden and develop more fully.
The Collaboration on Bridging Continuous and Discrete Optimization
is modeled on the existing DIMACS/Simons
Collaboration in Cryptography that began in 2015 and was the
first such partnership between the two centers. In addition to
DIMACS and the Simons Institute, the Collaboration is coordinating
workshops with the TRIPODS Institute for Optimization and Learning
at Lehigh University and with a month-long program on Mixed
Integer Nonlinear Programming sponsored by the Centre de Recherches
Mathématiques (CRM). Other workshops will coordinate with and
relate to future programs at the Simons Institute on Foundations
of Data Science and Geometry of
Polynomials.
The DIMACS/Simons Collaboration on Bridging Continuous and Discrete
Optimization is funded by the National Science Foundation as a
research coordination network under award CCF-
1740425. The Simons Institute program is supported in part by
a grant from the Simons Foundation.
Go here
to add yourself to the mailing list for the DIMACS Special Focus on
Bridging Continuous and Discrete Optimization.
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