Quadratic programming is a special type of mathematical programming problem.
Quadratic programming problem can be formulated like this:
Assume x belongs to Rn space.
Minimize (with respect to x)
0.5 x' E x + f' x
with the following boundary constraints (if there exists an answer then it satisfies these):
(1) A*x <= b (2) C*x = d (optional)
The (n x n) matrix E is usually positive semidefinite.
(this article needs a lot more work..)