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Regular version of the site

The clique problem for graphs with a few eigenvalues of the same sign

Optimization Letters. 2015. Vol. 9. No. 5. P. 839-843.

The quadratic programming problem is known to be NP-hard for Hessian matrices with only one negative eigenvalue, but it is tractable for convex instances. These facts yield to consider the number of negative eigenvalues as a complexity measure
of quadratic programs. We prove here that the clique problem is tractable for two variants of its Motzkin-Strauss quadratic formulation with a fixed number of negative eigenvalues (with multiplicities).