Abstract / Description of output
We consider the complex cut polytope: the convex hull of Hermitian rank 1 matrices xxH, where the elements of x∈Cn are mth unit roots. These polytopes have applications in MAX-3-CUT, digital communication technology, angular synchronization and more generally, complex quadratic programming. For m=2, the complex cut polytope corresponds to the well-known cut polytope. We generalize valid cuts for this polytope to cuts for any complex cut polytope with finite m>2 and provide a framework to compare them. Further, we consider a second semidefinite lifting of the complex cut polytope for m=∞. This lifting is proven to be equivalent to other complex Lasserre-type liftings of the same order proposed in the literature, while being of smaller size. Our theoretical findings are supported by numerical experiments on various optimization problems.
Original language | English |
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Journal | Mathematical programming |
Publication status | Published - 5 Sept 2024 |