On the search of the shape parameter in radial basis functions using univariate global optimization methods

• Published in: Journal of global optimization Vol. 79; no. 2; pp. 305 - 327
• Main Authors: Cavoretto, R., De Rossi, A., Mukhametzhanov, M. S., Sergeyev, Ya. D.
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.02.2021; Springer; Springer Nature B.V
• Subjects: Algorithms; Analysis; Computer Science; Global optimization; Interpolation; Mathematical optimization; Mathematics; Mathematics and Statistics; Operations Research/Decision Theory; Optimization; Parameters; Radial basis function; Real Functions; Technology application; Global optimization; 65K05; Shape parameter; 65D05; RBF interpolation; 90C26; 65D15

In this paper we consider the problem of finding an optimal value of the shape parameter in radial basis function interpolation. In particular, we propose the use of a leave-one-out cross validation (LOOCV) technique combined with univariate global optimization methods, which involve strategies of g...