If you are new to MATLAB, then if someone gives you highly optimized code to do this will be useless. You won't understand it, and it would take a couple of pages of explanation to get you to understand what it does, and you still won't be able to write a similar function yourself the next time. Yes, the objective is a quadratic functional of the vector w, with linear constraints. So you should be able to write this as a call to quadprog. But it sounds as if you are asking how to write this for your own optimizer.
Instead, just learn to write the objective using LOOPS. Loops are simple. And the call to optimize it, if you were using a tool like fmincon will be simple, but any other tool that allows a linear equality constraint and bound constraints would suffice.
