Sharp projected threshold for the nonlinear scheme

Determine whether the projected filtered reflected-gradient scheme admits the sharp universal step-size threshold \(\lambda L<1/\sqrt3\) for general monotone Lipschitz variational inequalities, rather than only in the unconstrained or partially analyzed affine-polyhedral settings.

Background

The unconstrained nonlinear problem is conjectured to have the sharp constant $1/\sqrt3$, while the projected case is explicitly left unresolved. The paper provides partial projected results, including the bounded-domain reflected range and dissipation-trading results for affine operators over polyhedral sets, but not the sharp general projected theorem.