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4OR
2010

Extended formulations in combinatorial optimization

11 years 5 months ago
Extended formulations in combinatorial optimization
This survey is concerned with the size of perfect formulations for combinatorial optimization problems. By "perfect formulation", we mean a system of linear inequalities that describes the convex hull of feasible solutions, viewed as vectors. Natural perfect formulations often have a number of inequalities that is exponential in the size of the data needed to describe the problem. Here we are particularly interested in situations where the addition of a polynomial number of extra variables allows a formulation with a polynomial number of inequalities. Such formulations are called "compact extended formulations". We survey various tools for deriving and studying extended formulations, such as Fourier's procedure for projection, Minkowski-Weyl's theorem, Balas' theorem for the union of polyhedra, Yannakakis' theorem on the size of an extended formulation, dynamic programming, and variable discretization. For each tool that we introduce, we present...
Michele Conforti, Gérard Cornuéjols,
Added 08 Dec 2010
Updated 08 Dec 2010
Type Journal
Year 2010
Where 4OR
Authors Michele Conforti, Gérard Cornuéjols, Giacomo Zambelli
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