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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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Minimize $f(A,B)$ s.t. $\text{exp}(A)^T \text{exp}(B)=J_K$

I have a function $f(A,B)$ that maps a pair of two (tall) matrices, $A$ and $B$, to a scalar cost that I want to minimize. $A$ and $B$ both have $K$ columns. I also want to impose a set of equality co …