SuperMann: a superlinearly convergent algorithm for finding fixed points of nonexpansive operators

Understand

Operator splitting techniques have recently gained popularity in convex optimization problems arising in various control fields.

• Being fixed-point iterations of nonexpansive operators, such methods suffer many well known downsides, which include high sensitivity to ill conditioning and parameter selection, and consequent low accuracy and robustness.
• As universal solution we propose SuperMann, a Newton-type algorithm for finding fixed points of nonexpansive operators.
• It generalizes the classical Krasnosel'skii-Mann scheme, enjoys its favorable global convergence properties and requires exactly the same oracle.