On the convexity for the range set of two quadratic functions

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

Given $n\times n$ symmetric matrices $A$ and $B$, Dines in 1941 proved that the joint range set $\{(x^{T}Ax,x^{T}Bx)|x\in {\mathbb{R}}^n\}$ is always convex. Our paper is concerned with…