Global optimization: beyond the Lipschitzian model

The authors present a new global optimization algorithm for minimizing a multivariate function subject to lower and upper bounds on the variables. The new algorithm uses the space-partitioning approach common to many Lipschitzian, interval-analysis, and Bayesian algorithms. It differs from these methods in its use of a new criterion for selecting regions for further search. This new criterion speeds up convergence by giving the algorithm the ability to perform both local and global search at the same time. Thus, once the global part of the algorithm finds the basin of convergence of the optimum, the local part quickly and automatically exploits it. The objective function is treated as a black box that need not be differentiable or Lipschitzian. Results are given for nine standard test functions