EDB β€” 1HB

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E3

[1HB] Prerequisites:[1F6],[1GB],[1H8].Let \(f,πœ‘\) be of class \(C^ 2\) in the open set \(A\), and let \(\overline x\) be a minimum point for \(f\) constrained to \(E_ a\); let \(πœ†\) be the Lagrange multiplier; let’s define \(h=f(x)+πœ†πœ‘(x)\), then

\[ βˆ€ v, vβ‹… βˆ‡ πœ‘(x)=0⟹ vβ‹… H vβ‰₯ 0 \]

where \(H\) is the Hessian matrix of \(h\).

Solution 1

[1HC]

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