Resolvent of a monotone operator
= Resolvent of a monotone operator
{title2=$J_{\tau A}=(I+\tau A)^{-1}$}
For an operator $A$, its resolvent with step $\tau>0$ is $J_{\tau A}=(I+\tau A)^{-1}$. A <maximal monotone operator> has an everywhere-defined single-valued <firmly nonexpansive mapping> as its resolvent. For $A=\partial f$, the resolvent is the <proximal map> of $\tau f$. This monotone-operator resolvent uses a different convention from the spectral resolvent of a linear operator.