A convergent simplicial algorithm with ω‐subdivision and ω‐bisection strategies

The simplicial algorithm is a kind of branch‐and‐bound method for computing a globally optimal solution of a convex maximization problem. Its convergence under the ω‐subdivision strategy was an open question for some decades until Locatelli and Raber (2000) proved it. In this paper, we modify their linear programming relaxation and give a different and simpler proof of the convergence. We also develop a new convergent subdivision strategy, and report numerical results of comparing it with existing strategies.