×

The simplex gradient and noisy optimization problems. (English) Zbl 0927.65077

Borggard, Jeff (ed.) et al., Computational methods for optimal design and control. Proceedings of the 2nd AFOSR workshop on Optimal design and control. Arlington, VA, USA, September 30 - October 3, 1997. Boston: Birkhäuser. Prog. Syst. Control Theory. 24, 77-90 (1998).
Summary: Many classes of methods for noisy optimization problems are based on function information computed on sequences of simplices. The method of J. A. Nelder and R. Mead [Computer J. 7, 308-313 (1965; Zbl 0229.65053)], multidirectional search, and implicit filtering methods are three such methods. The performance of these methods can be explained in terms of the difference approximation of the gradient implicit in the function evaluations. Insight can be gained into choice of termination criteria, detection of failure, and design of new methods.
For the entire collection see [Zbl 0901.00062].

MSC:

65K05 Numerical mathematical programming methods
90C30 Nonlinear programming

Citations:

Zbl 0229.65053

Software:

IMFIL
PDFBibTeX XMLCite