Editing Quadratic programming (section)

===Constrained least squares===

As a special case when {{math|''Q''}} is [[positive definite matrix|symmetric positive-definite]], the cost function reduces to least squares:
:{| cellspacing="10"
|-
| minimize
| <math>\tfrac{1}{2} \| R \mathbf{x} - \mathbf{d}\|^2 </math>
|-
| subject to
| <math>A \mathbf{x} \preceq \mathbf{b},</math>
|}
where {{math|1=''Q'' = ''R''<sup>T</sup>''R''}} follows from the [[Cholesky decomposition]] of {{math|''Q''}} and {{math|1='''c''' = −''R''<sup>T</sup> '''d'''}}. Conversely, any such [[constrained least squares]] program can be equivalently framed as a quadratic programming problem, even for a generic non-square {{math|''R''}} matrix.