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.
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Lewis, R. M., and Torczon, V., Rank Ordering and Positive Bases in Pattern Search Algorithms, SIAM Journal on Optimization.
Torczon, V., On the Convergence of Pattern Search Algorithms, SIAM Journal on Optimization, Vol. 7, pp. 1–25, 1997.
Torczon, V., On the Convergence of the Multidirectional Search Algorithm, SIAM Journal on Optimization, Vol. 1, pp. 123–145, 1991.
Dennis, J. E., and Torczon, V., Direct Search Methods on Parallel Machines, SIAM Journal on Optimization, Vol. 1, pp. 448–474, 1991.
Coope, I. D., and Price, C. J., On the Convergence of Grid-Based Methods for Unconstrained Minimization, Research Report 180, Department of Mathematics, University of Canterbury, Christchurch, New Zealand.
Coope, I. D., and Price, C. J., Convergent Frame-Based Quasi-Newton Methods (to appear).
Conn, A., Scheinberg, K., and Toint, P. L., On the Convergence of Derivative-Free Methods for Unconstrained Optimization, Approximation Theory and Optimization, Edited by M. D. Buhmann and A. Iserles, Cambridge University Press, Cambridge, England, pp. 83–108, 1997.
Powell, M. J. D., Direct Search Algorithms for Optimization Calculations, Acta Numerica, Vol. 7, pp. 287–336, 1998.
Davis, C., Theory of Positive Linear Dependence, American Journal of Mathematics, Vol. 76, pp. 733–746, 1954.
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Coope, I.D., Price, C.J. Frame Based Methods for Unconstrained Optimization. Journal of Optimization Theory and Applications 107, 261–274 (2000). https://doi.org/10.1023/A:1026429319405
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DOI: https://doi.org/10.1023/A:1026429319405