Adaptive diagonal curves and their implementation

The problem of a minimal description of a function f(x) over a multidimensional hyperinterval is considered. Particularly, global optimisation problems are discussed. Properties of the partition strategies that are traditionally used in the framework of the diagonal approach for solving multidimensional global optimisation problems are analysed. A new type of space-filling curves, adaptive diagonal curves, is described. It is shown that the application of these curves allows to solve the minimal description problem efficiently. Implementation of adaptive diagonal curves is also discussed.