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odlgroup / odl

Operator Discretization Library https://odlgroup.github.io/odl/

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primal_dual_hybrid_gradient solver: why compute derivative ?

Zeqiang-Lai opened this issue · comments

commented

I just could not make correspondence between the math and implementation of PDHG.

It seems that we do not need to compute gradient when update x

image

odl/odl/solvers/nonsmooth/primal_dual_hybrid_gradient.py

Line 282 in 0b088df

L.derivative(x).adjoint(y, out=primal_tmp)

commented

The derivative of a linear operator is the operator itself, so this surely doesn't harm anything. On the other hand, the code in this form also works for a non-linear operator, e.g., $Lx = A x + a$ with $A$ being linear, where "works" means that the iteration has the correct fixed points.