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The DIRECT algorithm of Jones et al. is a simple and effective Lipschitzian-based global optimization algorithm which does not need the evaluation of gradients. However, the local convergence rate is relatively slow when compared to popular quasi-Newton techniques. By incorporating the judicious use of gradients, modifications are proposed that result in a new algorithm. This new algorithm still covers effectively the design space and eliminates regions which are non-optimal but has the benefit or a fast local convergence rate. A comparison is made using six standard test problems showing that utilization of gradients is beneficial not only for convergence but also during the first few iterations.

A modification to Jones' global optimization algorithm for fast local convergence