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Tom.Reding (talk | contribs) m +{{Authority control}} (1 ID from Wikidata); WP:GenFixes & cleanup on |
→Least squares: Clarify that least squares are constrained |
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where {{math|'''x'''<sup>T</sup>}} denotes the vector [[transpose]] of {{math|'''x'''}}, and the notation {{math|''A'''''x''' ⪯ '''b'''}} means that every entry of the vector {{math|''A'''''x'''}} is less than or equal to the corresponding entry of the vector {{math|'''b'''}} (component-wise inequality).
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As a special case when {{math|''Q''}} is [[positive definite matrix|symmetric positive-definite]], the cost function reduces to least squares:
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| <math>A \mathbf{x} \preceq \mathbf{b},</math>
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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.
===Generalizations===
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