I'm interested in the optimization problem
$$\begin{array}{ll} \text{maximize} & x^T M \, x\\ \text{subject to} & \| x \| \leq 1\\ & x \geq 0\end{array}$$
where $M$ is positive definite. As I understand it, this isn't a convex problem, but the constraints should define a convex set. Is there a well-known way of solving this sort of problem?
For those curious about how I might have gotten here: I have $c$ sensors, each of which has $k$ features. I want to find a convex combination of the $k$ features per sensor that maximizes the distance between some patterns over the sensors.