Optimization of a particular function - Is it only quadratic ?

[AlbFrigerio]

Hello everyone, I've a "strange" question about function optimization.

I have a matrix X (size(X)=[m,n]) of known values and a vector y
(size(y)=[n,1]) of unknown ones. I want to optimize the function f(y) = prod
(X*y) w.r.t y , with the simplex type constraints ( sum(y)=1 and 0 \leq y
\leq 1 ) .

I've already used the Octave functions sqp, qp, linesearch, etc. , and
everything works (sometimes too slow, but I used very huge matrices) . I've
a different theoretical question: a friend of mine believes that my function
f is obviously quadratic but to me it is not so obvious (clearly X*y doesn't
harm me, the problem is the product of the vector (X*y) ) . 

Have you already seen a function like mine one, so that I can understand if
it is quadratic or not and, in positive case, study what matrices/vectors
use in the qp function to reach the solution?

Thank you so much,
   Alberto
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