User:Sintel/CTE tuning: Difference between revisions
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<math> | <math> | ||
\begin{align} | \begin{align} | ||
\underset{g}{\text{minimize}} & \quad \| g\mathrm{MW} - j\mathrm{W} \|^2 \\ | |||
\text{subject to} & \quad \phantom{\|} g\mathrm{MV} = j\mathrm{V} \\ | |||
\end{align} | \end{align} | ||
</math> | </math> | ||
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<math> | <math> | ||
\begin{align} | \begin{align} | ||
\underset{g}{\text{minimize}} & \quad \left\| \mathrm{A}g^{\mathsf T} - b \right\|^2 \\ | |||
\text{s.t.} & \quad \phantom{\|} \mathrm{C}g^{\mathsf T} = d \\ | |||
\end{align} | \end{align} | ||
</math> | </math> | ||
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</math> | </math> | ||
Where we introduced the vector of lagrange multipliers | Where we introduced the vector of lagrange multipliers <math>\lambda</math>, with size equal to the number of constraints. The lagrange multipliers have no concrete meaning for the resulting tuning, so they can be ignored. | ||
The problem is feasible if rank (V) ≤ rank (M). | The problem is feasible if rank (V) ≤ rank (M). |