How to derive efficient frontier by maximizing the utility function?

Hey,

I want derive the efficient frontier according to the mean varaince framework by maximizing the utility function U = w'R - (a/2) * w'Cw, where w is the weight vector, R the vector of expected return of the assets, a the risk aversion coefficient and C the covariance matirx of returns. Furthermore it should be maximized with respect to the weigths summing up to 1 and non negative w. Basically I should maximize the problem for different levels of "a" in order to obtain the frontier. My problem is that I don't know how to do this. I tried to use fmincon for -U, but the results weren't correct. Does anybody has an idea how derive the frontier in this way or which optimization function I should use? Thank you!