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Authors:Lennart Frimannslund: University of Bergen, Norway
Trond Steihaug: University of Bergen, Norway
Publication title:A New Generating Set Search Method for Unconstrained Optimisation
Conference:Nordic MPS 2004. The Ninth Meeting of the Nordic Section of the Mathematical Programming Society
Publication type: Abstract
Article No.:013
Abstract:Generating set searches, a class of derivative-free optimisation methods, has been an area of active research in recent years, much caused by the development of convergence theory. However, although these methods are usually easy to implement, robust and provably convergent in most cases, their attractiveness suffers from the fact that they are slow when it comes to convergence. Usually these methods do not take the local topography of the objective function into account.

We present a new algorithm which is a modification to a well known generating set search method, Compass Search. The new algorithm tries to adapt its search directions to the local topography by accumulating curvature information about the objective function as the search progresses. We present some theory regarding its properties, as well as numerical results that show our algorithm to outperform Compass Search most of the time, sometimes by significant relative margins, on noisy as well as smooth problems. In addition, preliminary numerical results indicate that we can exploit the sparsity information of the Hessian matrix. Thus allowing us to solve relatively large problems using methods in this class.

No. of pages:1
Series:Linköping Electronic Conference Proceedings
ISSN (print):1650-3686
ISSN (online):1650-3740
Publisher:Linköping University Electronic Press, Linköpings universitet

Lennart Frimannslund, Trond Steihaug (2004). A New Generating Set Search Method for Unconstrained Optimisation, Nordic MPS 2004. The Ninth Meeting of the Nordic Section of the Mathematical Programming Society;article=013 (accessed 4/23/2014)