Optimization by direct search: New perspectives on some Classical and modern methods.

*(English)*Zbl 1059.90146The paper is a well-written and sophisticated review on direct search methods, i.e. unconstrained optimization techniques which do not explicitely use derivatives. It starts with a brief historical overview about direct search methods and discusses several real-life applications of them.

The main goal of the review is to give a unified presentation of a large number of direct research methods and to analyze their convergence properties. In particular, some critical arguments (e.g. the techniques were based on heuristics, the methods were slow to converge, there were no mathematical analysis to accompany them) are addressed. Finally, extensions to problems with bound, linear and nonlinear constraints are presented.

The main goal of the review is to give a unified presentation of a large number of direct research methods and to analyze their convergence properties. In particular, some critical arguments (e.g. the techniques were based on heuristics, the methods were slow to converge, there were no mathematical analysis to accompany them) are addressed. Finally, extensions to problems with bound, linear and nonlinear constraints are presented.

Reviewer: Jan-Joachim Ruckmann (Puebla)

##### MSC:

90C56 | Derivative-free methods and methods using generalized derivatives |

90C30 | Nonlinear programming |