A generating set search method using curvature information |
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Authors: | Lennart Frimannslund Trond Steihaug |
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Institution: | (1) Department of Informatics, University of Bergen, Bergen, Norway |
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Abstract: | Direct search methods have been an area of active research in recent years. On many real-world problems involving computationally
expensive and often noisy functions, they are one of the few applicable alternatives. However, although these methods are
usually easy to implement, robust and provably convergent in many cases, they suffer from a slow rate of convergence.
Usually these methods do not take the local topography of the objective function into account. We present a new algorithm
for unconstrained optimisation which is a modification to a basic generating set search method. 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.
The curvature information is accumulated over a region thus smoothing out noise and minor discontinuities. We present some
theory regarding its properties, as well as numerical results. Preliminary numerical testing shows that the new algorithm
outperforms the basic method most of the time, sometimes by significant relative margins, on noisy as well as smooth problems.
This work was supported by the Norwegian Research Council (NFR). |
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Keywords: | Unconstrained optimisation Derivative-free optimisation Pattern search Generating set search |
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