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Quadratic Functions, Optimization, and Quadratic Forms

Quadratic Functions, Optimization, and Quadratic Forms

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Notice in the general model QP that we can always presume that Q is a symmetric matrix, because: xT Qx = 1 x T (Q + QT)x 2 and so we could replace Q by the symmetric matrix Q¯ := 1 2 (Q + QT). Now suppose that f (x):= 1 x T Qx + c T x 2 where Q is symmetric. Then it is easy to see that: ∇f (x)=Qx + c and H(x)=Q.

  Model, Quadratic

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