Pseudorandom lattices for global optimization

Rationalization processes are proposed to improve uniformity in small samples for pseudorandom lattices in (0, 1)ⁿ constructed from sequences produced by random number generators. On this basis, the space filtration and space contraction algorithms are developed for the solution of multimodal global optimization problems. Strong convergence to the global minimum value and convergence in measure onto the set of all global minimizers are proved. Numerical experiments are presented to illustrate a better uniformity provided by a rationalization process and the use of the space filtration algorithm for global optimization.