The Complexity of KKT Points of Quadratic Programs with Polynomially-Bounded Coefficients

Abstract

Computing a Karush-Kuhn-Tucker (KKT) point of a quadratic polynomial over the unit hypercube is known to be $CLS$-complete, when the coefficients of the polynomial are encoded in binary. We prove that the problem remains $CLS$-complete even when the coefficients are encoded in unary. This is the first problem proven to remain $CLS$-hard when the input is given in unary.