# Maximizing a Strictly Convex Quadratic Function Over a Convex Set

I need to solve a special case of non-convex QCQP (Quadratically Constrained Quadratic Programming) with the general form:

\begin{align} & \max {x^T}{A_o}x \\ & \text{s.t.}\left\{ \begin{matrix} {x^T}{A_i}x+{x^T}{a_i}+{c_i}\le 0 & i=1,\ldots,n \\ x\in L(x) & {} \\ x\ge 0 & {} \\ \end{matrix} \right. \\ \end{align}

Where $L(x)$ is a set of linear constraints and $A_o,A_1,\ldots,A_n\succ 0$ (positive definite). It basically involves maximizing a convex quadratic function over a convex set. I know that the solution to this problem takes place at the boundaries of the convex set and that standard methods would lead to a local optimum for such a problem. I need to know that besides from heuristics, are there any solution methods that could globally solve such a problem?