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Definition: Quadratic Programming Problem
Quadratic programming problems has a general form as follow:
$$\begin{align*} &\text{minimize }& \frac{ 1 }{ 2 } \transpose{ \b{x}} \b{Q} \b{x} \br &\text{subject to }& \b{Ax} = \b{b}\br \end{align*}$$
where $\b{Q} > 0$, $\b{A} \in \R^{m \times n}$, $m < n$, $\rank{ \b{A}} = m $.
Its global minimizer is
$$\b{x}^* = \inv{ \b{Q}} \transpose{ \b{A}} \inv{(\b{A} \inv{ \b{Q}} \transpose{ \b{A}})} \b{b}$$
In the special case where $\b{Q} = \b{I}_n $, the problem is reduced to the problem described in section 12.3.
$$\b{x}^* = \transpose{ \b{A}} \inv{(\b{A} \transpose{ \b{A}})} \b{b} $$