Global optimization of costly non-convex functions with financial applications (Q2740069)

The authors consider the problem of finding the global minimum when there are several local minima and each function value takes considerable CPU time to compute. Derivatives are most often hard to obtain that is why this paper deals with algorithms make no use of such information. The authors implement the algorithm by \textit{M. J. D. Powell} [Müller, M. W. (ed.) et al., New developments in approximation theory. 2nd international Dortmund meeting (IDoMAT) '98, Germany, February 23-27, 1998. Basel: Birkhäuser. ISNM, Int. Ser. Numer. Math. 132, 215--232 (1999; Zbl 0958.41501)] based on the use of radial basis functions and the Efficient Global Optimization method by \textit{D. R. Jones, M. Schonlau} and \textit{W. J. Welch} [J. Global Optim. 13, No. 4, 455--492 (1998; Zbl 0917.90270)] together with DIRECT and constrained DIRECT algorithms in the TOMLAB optimization environment by \textit{K. Holmström} [Advanced Modeling and Optimization, 1(1), 47--69 (1999); Theory Stoch. Process. 5(21), No. 1-2, 51--63 (1999; Zbl 0947.90131)]. The applications of these global optimization methods for parameter estimation in trading algorithms and in the models for time series prediction are presented.