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A generating set search method exploiting curvature and sparsity

Lennart Frimannslund (lennart.frimannslund***at***ii.uib.no)
Trond Steihaug (trond.steihaug***at***ii.uib.no)

Abstract: Generating Set Search method are one of the few alternatives for optimising high fidelity functions with numerical noise. These methods are usually only efficient when the number of variables is relatively small. This paper presents a modification to an existing Generating Set Search method, which makes it aware of the sparsity structure of the Hessian. The aim is to enable the efficient optimisation of functions with a relatively large number of variables. Numerical results show a decrease in the number function evaluation it takes to reach the optimal solution, sometimes by significant margins, on noisy as well as smooth problems, for a modest as well as relatively large number of variables.

Keywords: Nonlinear optimization, derivative-free optimization, pattern search, generating set search, sparsity

Category 1: Nonlinear Optimization (Unconstrained Optimization )

Citation: In Proceedings of the Ninth Meeting of the Nordic Section of the Mathematical Programming Society, pages 57-71. Linköping University Electronic Press. Linköping, Sweden, 2004. URL: http://www.ep.liu.se/ecp/014/004/index.html

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Entry Submitted: 01/04/2005
Entry Accepted: 01/04/2005
Entry Last Modified: 01/04/2005

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