The globally convexized filled functions for global optimization

Abstract

A new filled function, the globally convexized filled function, is proposed. The value of this function tends to positive infinity as the norm of the variable vector tends to infinity, and it has no stationary point in the region in which the objective function value is greater than or equal to the least value found so far, but it does have a minimizer (not only along the radius direction from the minimizer with the least objective function value found so far, like filled function found earlier by Ge) in the region in which the objective function value is less than the least value found so far, but with a prefixed minimizer. How to adjust parameters in the filled function is considered. Such a filled function can be appropriately combined with stochastic stopping rules proposed by Boender, Rinnooy Kan, and Timmer. The computational results show that this algorithm is quite efficient and reliable. © 1990.