A one-parameter filled function method applied to nonsmooth constrained global optimization

In this paper, we propose a filled function method for solving nonsmooth constrained global optimization problems. Based on a new definition of the filled function, a more practical one-parameter filled function is constructed which overcomes some drawbacks of the previous filled functions. Then a corresponding algorithm is presented. It attains a local minimizer by implementing a local search procedure, and finds a better local minimizer gradually by optimizing the filled function constructed on the minimizer, previously found. By repeating these steps, a global minimizer is obtained. Numerical experiments are presented to show the practicability of the proposed filled function method. In the end, extension conceivable applications are given in order to evaluate the merits of this method.