%0 Journal Article %1 Lewis2000Direct %A Lewis, Robert Michael %A Torczon, Virginia %A Trosset, Michael W. %D 2000 %J Journal of Computational and Applied Mathematics %K direct-search optimisation parameter-estimation review %N 1 %P 191 - 207 %R https://doi.org/10.1016/S0377-0427(00)00423-4 %T Direct search methods: then and now %U http://www.sciencedirect.com/science/article/pii/S0377042700004234 %V 124 %X We discuss direct search methods for unconstrained optimization. We give a modern perspective on this classical family of derivative-free algorithms, focusing on the development of direct search methods during their golden age from 1960 to 1971. We discuss how direct search methods are characterized by the absence of the construction of a model of the objective. We then consider a number of the classical direct search methods and discuss what research in the intervening years has uncovered about these algorithms. In particular, while the original direct search methods were consciously based on straightforward heuristics, more recent analysis has shown that in most — but not all — cases these heuristics actually suffice to ensure global convergence of at least one subsequence of the sequence of iterates to a first-order stationary point of the objective function.

@article{Lewis2000Direct, abstract = {We discuss direct search methods for unconstrained optimization. We give a modern perspective on this classical family of derivative-free algorithms, focusing on the development of direct search methods during their golden age from 1960 to 1971. We discuss how direct search methods are characterized by the absence of the construction of a model of the objective. We then consider a number of the classical direct search methods and discuss what research in the intervening years has uncovered about these algorithms. In particular, while the original direct search methods were consciously based on straightforward heuristics, more recent analysis has shown that in most — but not all — cases these heuristics actually suffice to ensure global convergence of at least one subsequence of the sequence of iterates to a first-order stationary point of the objective function.}, added-at = {2019-07-09T17:14:19.000+0200}, author = {Lewis, Robert Michael and Torczon, Virginia and Trosset, Michael W.}, biburl = {https://www.bibsonomy.org/bibtex/291c39a83b0f3230906b0a53f3efcf045/karthikraman}, description = {Direct search methods: then and now - ScienceDirect}, doi = {https://doi.org/10.1016/S0377-0427(00)00423-4}, interhash = {a20b9e047319f15b87fc447df58c25bd}, intrahash = {91c39a83b0f3230906b0a53f3efcf045}, issn = {0377-0427}, journal = {Journal of Computational and Applied Mathematics}, keywords = {direct-search optimisation parameter-estimation review}, note = {Numerical Analysis 2000. Vol. IV: Optimization and Nonlinear Equations}, number = 1, pages = {191 - 207}, timestamp = {2019-07-09T17:14:19.000+0200}, title = {Direct search methods: then and now}, url = {http://www.sciencedirect.com/science/article/pii/S0377042700004234}, volume = 124, year = 2000 }