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Equal Angle Distribution of Polling Directions in Direct-Search Methods

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  • Benjamin Van Dyke

Abstract

The purpose of this paper is twofold: first, to introduce deterministic strategies for directional direct-search methods, including new instances of the mesh adaptive direct-search (M ADS ) and the generating set search (G SS ) class of algorithms, which utilize a nice distribution of Po LL directions when compared to other strategies, and second, to introduce variants of each algorithm which utilize a minimal positive basis at each step. The strategies base their Po LL directions on the use of the QR decomposition to obtain an orthogonal set of directions or on using the equal angular directions from a regular simplex centered at the origin with vertices on the unit sphere. Test results are presented on a set of smooth, nonsmooth, unconstrained, and constrained problems that give comparisons between the various implementations of these directional direct-search methods.

Suggested Citation

  • Benjamin Van Dyke, 2014. "Equal Angle Distribution of Polling Directions in Direct-Search Methods," Journal of Optimization, Hindawi, vol. 2014, pages 1-15, July.
    • Handle: RePEc:hin:jjopti:619249
    DOI: 10.1155/2014/619249
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    References listed on IDEAS

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    1. L.-Z. Lu & C.E.M. Pearce, 2000. "Some New Bounds for Singular Values and Eigenvalues of Matrix Products," Annals of Operations Research, Springer, vol. 98(1), pages 141-148, December.
    2. Benjamin Dyke & Thomas J. Asaki, 2013. "Using QR Decomposition to Obtain a New Instance of Mesh Adaptive Direct Search with Uniformly Distributed Polling Directions," Journal of Optimization Theory and Applications, Springer, vol. 159(3), pages 805-821, December.
    3. I. D. Coope & C. J. Price, 2000. "Frame Based Methods for Unconstrained Optimization," Journal of Optimization Theory and Applications, Springer, vol. 107(2), pages 261-274, November.
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