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Normalize SR-PDE and STR-PDE objective functionals #3

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AlePalu opened this issue Oct 24, 2023 · 0 comments
Open

Normalize SR-PDE and STR-PDE objective functionals #3

AlePalu opened this issue Oct 24, 2023 · 0 comments

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@AlePalu
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AlePalu commented Oct 24, 2023

As for 956ba75, fpirls_init() initializes the status of SQR-PDE for the first FPIRLS iteration using the normalized SR-PDE functional

$$J(f, \boldsymbol{\beta}) = \frac{1}{n} \sum_{i=1}^n (y_i - \boldsymbol{x}_i^\top \boldsymbol{\beta} - f(\boldsymbol{p}_i))^2 + \frac{\lambda_{\mathcal{D}}}{2} \int_{\mathcal{D}} (Lf - u)^2.$$

Moreover FPIRLS uses the not-normalized SR-PDE version in its internals. This is not consistent. Need to write the SR-PDE and STR-PDE solvers in their normalized version.

@AlePalu AlePalu changed the title Normalize SR-PDE and STR-PDE objective functional Normalize SR-PDE and STR-PDE objective functionals Oct 24, 2023
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