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Shifted Composite L2 Norm #124
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Shifted Composite L2 Norm #124
MaxenceGollier
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Co-authored-by: Dominique <[email protected]>
I think this is ready for another round of review @dpo |
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Implementation of the proximal operator of a composite term$||Ax+b||_2$ . This is different from other operators of this library in the fact that shifts are no longer simply $\psi(x+s)$ for some non-differentiable function $\psi$ .
Hence, some abstract types are added in ShiftedProximalOperators.jl.
In practice, such proximal operators are useful when we want to make a model of a penalty term$x \xrightarrow{} ||c(x)||_2$ . The first-order model of the penalty term is then $s \xrightarrow{} ||c(x) + J(x)s||_2$ .
As mentionned above, the shift is no longer simply$\psi(x+s)$ . Hence, we add a CompositeNormL2 struct which mimics the unshifted function and implements $x\xrightarrow{} ||c(x)||_2$ . On shifts, this transforms to a ShiftedCompositeNormL2 struct which implements $s\xrightarrow{} ||c(x)+J(x)s||_2$ .