The Hamiltonian Cycle Problem (HCP) is the problem to find a cycle in a graph such that all vertices are visited exactly once. This problem is easily stated, but unfortunately it's an extremely difficult integer programming problem.
In this talk I will present a nonconvex quadratic formulation of the HCP, together with the Branch-and-Cut framework that guides the interior-point solver towards an integer solution.
A preliminary implementation exists, and numerical results are given for different types of cutting planes. The results suggest that the nonconvex quadratic formulation outperforms a linear formulation for large scale problems.
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