Update Pock-Chambolle to match 2011 paper#52
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klamike
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May 12, 2026
gdalle
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| > Pock, Thomas, and Antonin Chambolle. "Diagonal preconditioning for first order primal-dual algorithms in convex optimization." *2011 International Conference on Computer Vision*. IEEE, 2011. [doi:10.1109/ICCV.2011.6126441](https://doi.org/10.1109/ICCV.2011.6126441) | ||
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| for matrix $K$ of size $m \times n$ and $\alpha \in [0, 2]$, the diagonal factors are |
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In our code the constraint matrix is called A
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Was just sticking to the Pock-Chambolle paper here. Also, we will use it for Q in the upcoming convex QP support (well, for K = [Q A'; A 0 ])
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| Following Lemma 2 of: | ||
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| > Pock, Thomas, and Antonin Chambolle. "Diagonal preconditioning for first order primal-dual algorithms in convex optimization." *2011 International Conference on Computer Vision*. IEEE, 2011. [doi:10.1109/ICCV.2011.6126441](https://doi.org/10.1109/ICCV.2011.6126441) |
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| column_power_sum(A, j, p) | ||
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| Return `sum_i |A[i, j]|^p`. Zero entries are treated as contributing `0` (not `0^0 = 1`), |
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I'm not sure why you say the initial implementation was incorrect. Doesn't LinearAlgebra.norm(x, p) take care of undoing the inner power at the end?
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Co-authored-by: Guillaume Dalle <22795598+gdalle@users.noreply.github.com>
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We
had the exponents swapped, andforgot to undo the outer power. This PR fixes the formulas to match the paper (except for the exponents, where we adopt the PDLP convention to be aligned with other solvers). It also adds a short section about it to the docs.Reusing the
diagonal_normfunction (while incorporating the correctness fix) would be extra work ((x^(1/p))^p), so we introduce a special helper for the column-power-sum (without the outer power).