Jon Lee (left), Daniel Dadus, and Jean-Philippe Richard.
Winner: Daniel Dadush, Georgia Institute of Technology
Paper: On the Chvátal-Gomory Closure of a Compact Convex Set
Authors: Daniel Dadush, Santanu S. Dey, and Juan Pablo Vielma
The paper shows that the Chvátal-Gomory closure of compact convex sets is a rational polytope. For the special case of rational polytopes, this is a well-known result. The new result includes the case of irrational polytopes and thus resolves a question that was posed by Schrijver (1980) and had remained open since. Solving this long-open question is already a wonderful contribution, finally completing the Chvátal-Gomory theory for polytopes. The paper goes beyond this and also provides a solution for arbitrary compact convex sets, completing the program started in a paper by Dey and Vielma (2010) for the case of ellipsoids and continued in an earlier paper by Dadush, Dey, and Vielma (2011) for the case of strictly convex bodies. The importance of this contribution lies in providing a foundation for a finite linear cutting plane theory for convex integer optimization.
The paper uses techniques from convex geometry and the geometry of numbers in an expertly way. In the proofs, the authors avoid explicit calculations in favor of soft analysis, including techniques from point-set topology, which makes the paper particularly elegant.
Matthias Koeppe (Chair), Jean-Philippe Richard, Katya Scheinberg