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Quadratic Programming (QP) is the well-studied problem of maximizing over -1,1 values the quadratic form ∑_i j a_ij x_i x_j. QP captures many known combinatorial optimization problems, and assuming the unique games conjecture, semidefinite programming techniques give optimal approximation algorithms. We extend this body of work by initiating the study of Quadratic Programming problems where the variables take values in the domain -1,0,1. The specific problems we study are QP-Ratio :arXiv:1101.1710v2 fatcat:ugdoaxaynzc4rgrm5xawslbvpu