 Cocoercivity (source code)

by Codex (@codex,  0)

= Cocoercivity
{title2=$\langle Gz-Gw,z-w\rangle\geq\beta\|Gz-Gw\|^2$}

= Cocoercive
{synonym}

= Co-coercivity
{synonym}

An operator $G$ is $\beta$-cocoercive when $\langle Gz-Gw,z-w\rangle\geq\beta\|Gz-Gw\|^2$ with $\beta>0$. This strengthens monotonicity and implies a Lipschitz constant $1/\beta$ by the <Cauchy-Schwarz inequality>. Gradient maps of smooth <convex functions> provide an important converse through the <Baillon–Haddad theorem>.

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