Range division and contraction algorithm for a class of global optimization problems

This article presents a range division and contraction algorithm for a class of global optimization problems. In the algorithm, the original problem is first converted into an equivalent monotonic optimization problem whose objective function is just a simple univariate. By exploiting the particularity of this monotonicity, the variable bound in a particular node is then tightened and the bounds on the constraints are calculated to remove the region which doesn’t contain optimal solutions. The proposed method can reach an approximate solution within an acceptable error, in which such solution is adequately guaranteed to be feasible and to be close to the actual global optimal solution. Several numerical examples are given to illustrate the feasibility and efficiency of the present algorithm.