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The method of Lagrange multipliers finds critical points (including maxima and minima) of a differentiable function subject to differentiable constraints.
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votes
How to choose between dual gradient descent and the method of Lagrangian multipliers?
We need to satisfy the KKT conditions(first order necessary conditions) in order to find the optimal solution.
KKT conditions for equality constraints:
$$
Stationary: \nabla_x \mathcal{L}(x,\lambda) …