Optimization has long been a source of both inspiration and applications
for geometers, and conversely, discrete and convex geometry have
provided the foundations for many optimization techniques, leading to a
rich interplay between these subjects. The purpose of the Workshop on
Discrete Geometry, the Conference on Discrete Geometry and Optimization,
and the Workshop on Optimization, held in September 2011 at the Fields
Institute, Toronto, was to further stimulate the interaction between
geometers and optimizers. This volume reflects the interplay between
these areas.
The inspiring Fejes Tóth Lecture Series, delivered by Thomas Hales of
the University of Pittsburgh, exemplified this approach. While these
fields have recently witnessed a lot of activity and successes, many
questions remain open. For example, Fields medalist Stephen Smale stated
that the question of the existence of a strongly polynomial time
algorithm for linear optimization is one of the most important unsolved
problems at the beginning of the 21st century. The broad range of topics
covered in this volume demonstrates the many recent and fruitful
connections between different approaches, and features novel results and
state-of-the-art surveys as well as open problems.