Hi， I want to solve a quadratic optimization problem defined as
$\min \|\bf{a^T}\bf{x}\|^2_2$
$s.t. \|\bf{x}\|_1=1$
$\ \ \ \ \ \ \ \ x_i\ge0,\ i=0,1,...,n-1$
$\ \ \ \ \ \ \ \ \bf{b}^T\bf{x}-C\le0$
where $\bf{x},\bf{a},\bf{b}\in\mathbb{R}^{n\times1}$ and their entries are positive. $C$ is a constant value with $C>0$.
I know it is easy but I can't solve it myself. Giving me some references is OK.
I found this problem is similar to Markowitz portfolio theory (right?), but I don't know anything about finance. Thanks!