### A semidefinite programming hierarchy for geometric packing problems

**de Laat, D ***(Technische Universiteit Delft)*

Thursday 18 July 2013, 10:00-10:30

Seminar Room 1, Newton Institute

#### Abstract

Geometric packing problems can be modeled as maximum independent set problems in infinite graphs. Computing the independence number is NP-hard. To get a chain of improving upper bounds for finite graphs one can formulate the problem as a polynomial optimization problem and then use the Lasserre hierarchy. We generalize this hierarchy to infinite graphs using conic optimization over cones of positive kernels and measures of positive type. For finite graphs it is known that the hierarchy attains the independence number after finitely many steps. We show that this is also true for the generalized hierarchy if the infinite graph corresponds to a packing problem. Based on joint work with Frank Vallentin.

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