On Separation of level sets for a pair of quadratic functions

Huu-Quang Nguyen, Ya-Chi Chu, Ruey-Lin Sheu

Given a quadratic function $f(x)=x^{T}Ax+2a^{T}x+a_0,$ it is possible that its level set $\{x\in {\mathbb{R}}^n:f(x)=0\}$ has two connected components and thus can be separated by the le…