A class of filled functions for box constrained continuous global optimization

In this paper we show that the unconstrained continuous global minimization problem cannot be solved by any algorithm, so we consider the box constrained continuous global minimization problem. We present a definition of filled function for the problem. Moreover, a new class of filled functions are constructed, which contains only one parameter. A randomized algorithm is designed to solve the box constrained continuous global minimization problem based on the filled function. Numerical experiments are presented to show the practicability of the algorithm.