Two new classes of filled functions

摘要

The filled function method is an effective approach to find the global minimizer. Two of the recently proposed filled functions are L(X) and L2(X). Having observed that the second term in L(X) or L2(X) may result in undesirable computational behaviors, in this paper we propose a new function L3(X). Having also realized that the essence of the mitigation is to eliminate the discontinuity, we propose another new function L4(X). Both theoretical analysis and numerical testing results are presented.