Direct search algorithms for optimization calculations. (English) Zbl 0911.65050

Powell, M. J. D.

Acta Numerica 7, 287-336 (1998).

The author gives an extensive survey about optimization calculations when first derivatives are not available. Three main techniques are employed for trying to achieve global convergence, namely line searches, trust regions and discrete grids. Thus the paper is a collection of essays on particular strategies and algorithms, in order to discuss the advantages, limitations and theory of several techniques. The main features of the methods are studied themselves, because an understanding of these features may be very helpful to the application of the methods and to future research. However, most of the algorithms are for the case when the variables are unconstrained. The subjects addressed in the paper are line search methods, the restriction of vectors of variables to discrete grids, the use of geometric simplices (including also the Nelder/Mead algorithm), conjugate direction procedures, trust regions algorithms that form linear or quadratic approximations to the objective function, and simulated annealing.
For the entire collection see [Zbl 0894.00025].

Reviewer: J.Terno (Dresden)

MSC:

65K05	Numerical mathematical programming methods
90C30	Nonlinear programming

Keywords:

search algorithms; optimization calculations without derivatives; global convergence; discrete grids; line search methods; Nelder/Mead algorithm; trust regions algorithms; simulated annealing

Software:

COBYLA2; DFO; BRENT