Continuous global optimization through the generation of parametric curves

In this paper we develop a new approach for solving a large class of global optimization problems. The objective function is only continuous, non-smooth and non-Lipschitzian, defined on a rectangle of RnRn. This approach is based on the generation, in the feasible set, of a family of parametrized curves satisfying certain properties combined with the one-dimensional Evtushenko algorithm. To accelerate the corresponding mixed algorithm, we have incorporated in a variant a Pattern Search-type deterministic local optimization method and in another variant a new stochastic local optimization method. Both variants have been applied to several typical test problems. A comparison with some well known methods is highlighted through numerical experiments.