Continuum-limit separation of vertex-weighted and unweighted values

Determine whether the strict separation observed between the discretized vertex-weighted and unweighted factor-revealing programs persists in the continuum limit, or whether the two sequences of optimal values converge to the same limit as the grid resolution tends to infinity.

Background

The paper defines the vertex-weighted and unweighted factor-revealing values by imposing progressively stronger monotonicity conditions on the cutoff curves. Both corresponding discretized optimization problems can be formulated as linear programs.

At every tested grid size, the unweighted program has a larger optimal value than the vertex-weighted program. The unresolved issue is whether this finite-grid separation remains nonzero after passing to arbitrarily fine grids, or whether the two discretized sequences have the same continuum limit.