Abstract
The present paper introduces the geometric rank as a measure for the quality of relaxations of certain combinatorial optimization problems in the realm of polyhedral combinatorics. In particular, this notion establishes a tight relation between the maximum stable set problem from combinatorial optimization, polynomial programming from integer non linear programming and norm maximization, a basic problem from convex maximization and computational convexity.
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Brieden, A., Gritzmann, P. (2003). On the Inapproximability of Polynomial-programming, the Geometry of Stable Sets, and the Power of Relaxation. In: Aronov, B., Basu, S., Pach, J., Sharir, M. (eds) Discrete and Computational Geometry. Algorithms and Combinatorics, vol 25. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-55566-4_13
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DOI: https://doi.org/10.1007/978-3-642-55566-4_13
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