Matching polytope

Matching polytope

Formulating and Solving Integer Programs

Published in Craig A. Tovey, Linear Optimization and Duality, 2020

Theorem 4.2.2 offers a possible loophole. There might be a higher dimensional polyhedron Q^ that has polynomially many facets, and projects down to Q. In the case of the TSP polytope, Yannakakis [303] proved that no symmetric such Q^ exists. This was a remarkable result because it does not rely on any assumption such as P≠NP. Later, Fiorini et al. [95] proved the stronger result, that any Q^ which projects to the TSP polytope, whether symmetric or not, must have exponentially many facets. Even more recently, Rothvoß [255] proved that the same is true for the matching polytope, despite the fact that optimization over the matching polytope can be done in polynomial time.

A new hybrid matheuristic optimization algorithm for solving design and network engineering problems

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Journal Information

Published in International Journal of Management Science and Engineering Management, 2018

G. Chagwiza, B. C. Jones, S. D. Hove-Musekwa, S. Mtisi

The incidence vector of M ⊆ E is a vector which satisfies if e ∊ M and if e ∉ M. The matching polytope P(G) of G is the convex hull of the perfect matching of G denoted as

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Formulating and Solving Integer Programs

A new hybrid matheuristic optimization algorithm for solving design and network engineering problems