 Solution

ID: past-exam-of-the-options-i-course-of-the-university-of-oxford/2009/f/f1/a/solution

λ_{1}, λ_{2}

such that

\nabla g (x_{0}) = λ_{1} \nabla f_{1} (x_{0}) + λ_{2} \nabla f_{2} (x_{0}) .

Equivalently

D g (x_{0}) = λ^{T} D f (x_{0})

. The rank assumption says the two constraint gradients are linearly independent; it rules out an abnormal constraint point.

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