Unless you place some further constraints on W values, there is no limit to how much 'f' can be reduced. The right answer would be minus infinity. For example, let W(1) = 1, w(2) = +2^50, w(3) = -2^50. Then the sum of the w's is 1 and f is -2^51+3 which is a huge negative number. If you restrict W to non-negative values, then the obvious answer is 3 without the necessity of using matlab.
To learn how to accomplish such a minimization in a general situation, read the documentation for 'fmincon' at:
http://www.mathworks.com/help/optim/ug/fmincon.html
