Nonnegative Quadratics over a Quadrant with a Bilinear Constraint

Yipeng Zhang, Yuyuan Ouyang, Boshi Yang

We study quadratic polynomials that are nonnegative on the non-compact set \[ F:=\{(x_1,x_2)\in\mathbb R^2:\ x_1\ge 0,\ x_2\ge 0,\ x_1x_2\le 1\}. \] All extreme rays of the cone of…