Multidimensional global optimization using the first derivatives

We propose a new multidimensional algorithm for solving global optimization problems with the objective function having Lipschitzean first derivatives and determined over a multidimensional interval. The method does not belong to the class of multistart algorithms. It is based on the following three new proposals and is an illustration how it is possible to generalize to the multidimensional case the one-dimensional algorithms belonging to the Classes of adaptive partition and characteristical global optimization methods. The first proposal is to estimate the local Lipschitz constants for derivatives in different subintervals of the search region during the course of optimization to provide a local tuning on the behavior of the objective function. The second one is a new partitioning scheme providing an efficient keeping of the search information. The last proposal is a way to calculate characteristics of multidimensional intervals to provide convergence to the global minimizers.