Non-Univalent Approximation of Peano Curve for Global Optimization

In this article, multi-dimensional global optimization problems are considered, where the objective function is supposed to be Lipschitz continuous, multiextremal and without a known analytic expression (black-box). Non-Univalent approximation of Peano curve to reduce the problem to a univariate one satisfying the Hölder condition is employed. Geometric frameworks for construction of global optimization algorithms are discussed. Numerical experiments executed on 100 test functions taken from the literature show a promising performance of the algorithms.