Quadratic programming is a special type of mathematical programming problem.
Quadratic programming problem can be formulated like this:
Assume x belongs to Rn space. The (n x n) matrix E is positive semidefinite.
Minimize (with respect to x)
f(x) = 0.5 x' E x + f' x
with the following constraints (if there exists an answer then it satisfies these):
(1) A*x <= b (inequality constraint) (2) C*x = d (equality contraint)
Since f(x) is a convex function, and constraints are linear functions, we have from optimization theory that for point x to be an optimum point it is necessary and sufficient that x is a Kuhn-Tucker point.
(this article needs a lot more work..)