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If you write the problem of finding the closest point to $x_0$ on the cone with a Lagrange multiplier, the solution must have the form $x = (\lambda A + I )^{-1}x_0$. If you start by diagonalizing $A$, the inverse can be computed efficiently and you can search for $\lambda$ by dichotomy. The algorithm will run in $O(n^2 \log{n})$log{1/\epsilon})$ |
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If you write the problem of finding the closest point to $x_0$ on the cone with a Lagrange multiplier, the solution must have the form $x = (\lambda A + I )^{-1}x_0$. If you start by diagonalizing $A$, the inverse can be computed efficiently and you can search for \lambda $\lambda$ by dichotomy. The algorithm will run in $O(n^2 \log{n})$ |
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If you write the problem of finding the closest point to $x_0$ on the cone with a Lagrange multiplier, the solution must have the form $x = (\lambda A + I )^{-1}x_0$. If you start by diagonalizing $A$, the inverse can be computed efficiently and you can search for \lambda by dichotomy. The algorithm will run in $O(n^2 \log{n})$ |
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