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From combinatorial optimization to real algebraic geometry and back
Povh, Janez, 1973-
In this paper we explain the relations between combinatorial optimization and real algebraic geometry with a special focus to quadratic assignment problem. We demonstrate how to write a quadratic ...optimization problem over discrete feasible set as a linear optimization problem over the cone of completely positive matrices. The later formulation enables hierarchy of approximations which rely on results from polynomial optimization, a sub-field of real algebraic geometry.
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