The DIMACS Special Focus on Bridging Continuous and Discrete Optimization is part of the DIMACS/Simons Collaboration on Bridging Continuous and Discrete Optimization, a Research Coordination Network led by DIMACS and the Simons Institute for the Theory of Computing to advance both the foundations and practical capabilities of optimization algorithms and methods.
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 meeting these challenges with innovative new methods improving performance guarantees that had stood for decades. 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.
The activities of the special focus will bring together computer scientists, mathematicians, operations researchers, engineers, statisticians, and algorithm developers with the aim of advancing the theoretiacl foundations and the practical performance of optimization methods in challenging real settings. The special focus will involve a large number of people in various scientific communities and expose them to new ideas, new problems, and new opportunities for collaboration.