A novel method for global minimization combined filled function method and dimensionality reduction technique

Abstract

This paper introduces a new filled function method based on the dimensionality reduction technique for the global minimization problem. By utilizing the so called α - dense curves, we first transform the original function of n-variables into a single variable function, and then minimize the transformed function with the filled function method. The constructed filled function contains just one parameter which can be adjusted readily during the iterative process. The theoretical properties of the filled function are discussed, and the filled function algorithm is given. At last, a few numerical experiments are included.