Review Note
Last Update: 05/01/2024 08:25 AM
Current Deck: TTK4135
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Second-order sufficient conditions
Suppose that \(x^*\) is a local solution and that the LICQ condition is satisfied. Let \(\lambda^*\) be the Lagrange multiplier vector for which the KKT conditions are satisfied. {{c1::Then
\[w^T \nabla^2_{xx} \mathcal{L} (x^*, \lambda^*) w > 0\]for all \[w \in \mathcal{C}(x^*, \lambda^*), w \neq 0\]}}
Suppose that \(x^*\) is a local solution and that the LICQ condition is satisfied. Let \(\lambda^*\) be the Lagrange multiplier vector for which the KKT conditions are satisfied. {{c1::Then
\[w^T \nabla^2_{xx} \mathcal{L} (x^*, \lambda^*) w > 0\]for all \[w \in \mathcal{C}(x^*, \lambda^*), w \neq 0\]}}
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