Quadratic Programming

Qudaratic programming (QP) is an optimization problem with the following objective:

Minimize

\begin{align*} f(x) = \frac 1 2 x^T Q x + c^T x \end{align*}

subject to,

\begin{align*} Ax \leq b \end{align*}

where,

1. \(x\) is a \(n\) dimensional vector and

2. \(Q\) is a \(n \times n\) symmetric matrix

   If \(Q\) isn't symmetric we can convert the QP problem into an equivalent QP problem were the \(Q' = (Q + Q^T) / 2\) is symmetric. So, there is no loss in generality in assuming symmetric \(Q\) and additionally, we get simpler formulas.