| # A Quadratic Program with Two Variables Consider the problem The problem is a quadratic program: the constraints are affine inequalities in the decision vector ; the objective function can be expressed as where We check that is positive semi-definite by computing its eigenvalue decomposition: and checking that the eigenvalues (appearing on the diagonal of ) are non-negative.
| Geometric view of the quadratic program above. The problem is a QP since the objective function is quadratic convex, and the constraints are affine inequalities.