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Frame Based Methods for Unconstrained Optimization

Author

Listed:
  • I. D. Coope

    (University of Canterbury)

  • C. J. Price

    (University of Canterbury)

Abstract

This paper describes a wide class of direct search methods for unconstrained optimization, which make use of fragments of grids called frames. Convergence is shown under mild conditions which allow successive frames to be rotated, translated, and scaled relative to one another.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:107:y:2000:i:2:d:10.1023_a:1026429319405
    DOI: 10.1023/A:1026429319405
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    Citations

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    Cited by:

    1. 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.
    2. A. Sanchez & Diego Martinez, 2011. "Optimization in Non-Standard Problems. An Application to the Provision of Public Inputs," Computational Economics, Springer;Society for Computational Economics, vol. 37(1), pages 13-38, January.
    3. C.J. Price & I.D. Coope, 2003. "Frame-Based Ray Search Algorithms in Unconstrained Optimization," Journal of Optimization Theory and Applications, Springer, vol. 116(2), pages 359-377, February.
    4. Ubaldo M. García-Palomares, 2020. "Non-monotone derivative-free algorithm for solving optimization models with linear constraints: extensions for solving nonlinearly constrained models via exact penalty methods," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(3), pages 599-625, October.
    5. Javaid Ali & Muhammad Saeed & Muhammad Farhan Tabassam & Shaukat Iqbal, 2019. "Controlled showering optimization algorithm: an intelligent tool for decision making in global optimization," Computational and Mathematical Organization Theory, Springer, vol. 25(2), pages 132-164, June.
    6. Árpád Bűrmen & Jernej Olenšek & Tadej Tuma, 2015. "Mesh adaptive direct search with second directional derivative-based Hessian update," Computational Optimization and Applications, Springer, vol. 62(3), pages 693-715, December.
    7. C.J. Price & I.D. Coope & D. Byatt, 2002. "A Convergent Variant of the Nelder–Mead Algorithm," Journal of Optimization Theory and Applications, Springer, vol. 113(1), pages 5-19, April.
    8. Charles Audet & Christophe Tribes, 2018. "Mesh-based Nelder–Mead algorithm for inequality constrained optimization," Computational Optimization and Applications, Springer, vol. 71(2), pages 331-352, November.
    9. Y. Diouane & S. Gratton & L. Vicente, 2015. "Globally convergent evolution strategies for constrained optimization," Computational Optimization and Applications, Springer, vol. 62(2), pages 323-346, November.
    10. Árpád Bűrmen & Iztok Fajfar, 2019. "Mesh adaptive direct search with simplicial Hessian update," Computational Optimization and Applications, Springer, vol. 74(3), pages 645-667, December.
    11. Benjamin Van Dyke, 2014. "Equal Angle Distribution of Polling Directions in Direct-Search Methods," Journal of Optimization, Hindawi, vol. 2014, pages 1-15, July.
    12. David W. Dreisigmeyer, 2018. "Direct Search Methods on Reductive Homogeneous Spaces," Journal of Optimization Theory and Applications, Springer, vol. 176(3), pages 585-604, March.

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