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Table 1 So far known integrality gap bounds for binary control approximation algorithms

From: Mixed-integer optimal control under minimum dwell time constraints

  Next-forced rounding (NFR) Sum-up rounding (SUR) SUR with vanishing constraints
\(C({n_\omega })= \) 1, see [21], \( \sum \nolimits _{i=2}^{{n_\omega }} \frac{1}{i}\), see [24], \(\lfloor {n_\omega }/2 \rfloor \), see [28]
  1. By vanishing constraints we refer to constraints of the form \(\omega _i(t)g(x(t))\le 0\), for \(i=1,\ldots ,{n_\omega }\) where g is a smooth function