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Mathematics - Geometry & Topology | Discrete Geometry and Optimization

Discrete Geometry and Optimization

Bezdek, Karoly, Deza, Antoine, Ye, Yinyu (Eds.)

2013, X, 336 p. 56 illus., 34 illus. in color.

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  • Contains a wide range of open problems, novel results, and state-of-the-art surveys 
  • Presents a snapshot of a rapidly evolving area on the boundary of discrete geometry and optimization
  • Reflects the broad and international participation at the Workshop on Discrete Geometry, Conference on Discrete Geometry and Optimization, and Workshop on Optimization

​​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.

Content Level » Research

Keywords » Carathéodory theorem - Combinatorics - Eigenvalue optimization - Minkowski spaces - SDP relaxation - polyhedral computations

Related subjects » Applications - Geometry & Topology

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