Generalize the regularized MAXBET algorithm’s behavior across regularization parameters

Determine whether the observed behavior of the NEPv approach for the $(2,1)$-norm-regularized MAXBET problem, as the regularization parameter $\alpha$ varies from small to sufficiently large values, can be generalized beyond the reported numerical experiments.

Background

The paper reports that the NEPv approach is comparatively easy to run for small and sufficiently large regularization parameters α\alpha, but encounters greater difficulty for intermediate values. The authors explain the large-α\alpha behavior theoretically: the regularization term dominates the original MAXBET objective, producing solutions close to minimizers of the perturbed (2,1)(2,1)-norm. However, they explicitly leave unresolved whether the full behavior observed as α\alpha increases from small values can be generalized.

References

It is not clear if the behavior for $\alpha$ varying from small up to certain point can be generalized but the behavior for sufficiently large $\alpha$ is generalizable.

— NEPv Approach for Optimization on Stiefel Manifold with the $(2,1)$-norm Regularization  (2609.26675 - Li et al., 22 Sep 2026) in Section 6, Numerical Experiments, discussion following Figure 1 (regularized MAXBET results)