Structure of Filled Functions: Why Gaussian and Cauchy Templates Are Most Efficient

Authors

Vyacheslav Kalashnikov, Tecnológico de Monterrey (ITESM)Follow
Vladik Kreinovich, The University of Texas at El PasoFollow
José Guadalupe Flores Muñiz, Universidad Autónoma de Nuevo LeónFollow
Nataliya Kalashnykova, Universidad Autónoma de Nuevo LeónFollow

Publication Date

12-2016

Comments

Technical Report: UTEP-CS-16-89

To appear in International Journal of Combinatorial Optimization and Informatics

Abstract

One of the main problems of optimization algorithms is that they often end up in a local optimum. It is, therefore, necessary to make sure that the algorithm gets out of the local optimum and eventually reaches the global optimum. One of the promising ways guiding one from the local optimum is prompted by the filled function method. It turns out that empirically, the best smoothing functions to use in this method are the Gaussian and Cauchy functions. In this paper, we provide a possible theoretical explanation of this empirical effect.