A generalization of ω-subdivision ensuring convergence of the simplicial algorithm

In this paper, we refine the proof of convergence by Kuno–Buckland (J Global Optim 52:371–390, 2012) for the simplicial algorithm with $\mathit{\omega }$ ‐subdivision and generalize their $\mathit{\omega }$ ‐bisection rule to establish a class of subdivision rules, called $\mathit{\omega }$ ‐k‐section, which bounds the number of subsimplices generated in a single execution of subdivision by a prescribed number k. We also report some numerical results of comparing the $\mathit{\omega }$ ‐k‐section rule with the usual $\mathit{\omega }$ ‐subdivision rule.