A Class of Augmented Filled Functions

The filled function method is an effective approach to find the global minimizer. Two of the recently proposed filled functions are H(X) and L₂(X). Although their numerical behavior is acceptable, they are not defined everywhere. This paper proposes a class of augmented filled functions with improved analyticity. Issues covered in the presented work include: theoretical properties, convergence analysis, geometric interpretation, algorithms, and numerical experiments. The overall performance of the new approach is comparable to the recently proposed ones.