 Solution

ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2022/discrete-mathematics-continuous-mathematics-and-probability-resit/5/b/i/solution

Write

(x^{T} b)^{2} = x^{T} b b^{T} x

and put

C = A - b b^{T}

, which is symmetric. Differentiating this quadratic form gives

\nabla g (x) = 2 C x = 2 A x - 2 (x^{T} b) b, H_{g} (x) = 2 (A - b b^{T}) .

Unlike

A

C

need not be a positive-definite matrix. Its behaviour must be checked before classifying the stationary point.

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