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Extend solver_L1RLS to solver_L1RLS_W #8

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RoyiAvital opened this issue Aug 19, 2017 · 1 comment
Open

Extend solver_L1RLS to solver_L1RLS_W #8

RoyiAvital opened this issue Aug 19, 2017 · 1 comment

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@RoyiAvital
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Hello,

Currently solver_L1RLS solves:

$$ 0.5 ||A x - b||^{2} + \lambda || x ||_{1} $$

Could it be extended to:

$$ 0.5 ||A x - b||^{2} + \lambda || W x ||_{1} $$

As done with other solvers?

Thank You.

@stephenbeckr
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You could solve that weighted problem with TFOCS using the fancier options, but in terms of directly extending solver_L1RLS, that would require replacing prox_l1 with a weighted version, and in general the weighted prox for l_1 is not computable in closed form (with a few exceptions, e.g., if W is diagonal or partial orthogonal... these are not directly implemented but you could make your own implementation or just make an explicit change-of-variables.

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