Maximal monotonicity of piecewise polyhedral mappings

What the math gives to ML

The paper gives a constructive elimination principle for maximal monotone operators whose graphs are piecewise polyhedral: after splitting the Hilbert space into retained and eliminated coordinates, the projected relation remains maximal monotone under a simple feasibility witness, without relative-interior constraint qualifications. Its proof uses Minty resolvents, exploiting that the resolvent is single-valued, nonexpansive, and piecewise affine. This suggests a stable implicit neural layer in which an auxiliary block is solved or eliminated through a fixed-point resolvent, while maximal monotonicity of the reduced input-output map provides well-posedness and nonexpansiveness guarantees.