On the convergence of grid-based methods for unconstrained optimization

SIAM Journal on Optimization

Volumn 11, Issue 4, 2001, Pages 859-869

  Coope, I D ^a   Price, C J ^a  

^a UNIVERSITY OF CANTERBURY   (New Zealand)

Author keywords

Convergence analysis; Derivative free optimization; Grid based optimization; Multidirectional search; Positive basis methods

Indexed keywords

EID: 0035623851     PISSN: 10526234     EISSN: None     Source Type: Journal    
DOI: 10.1137/S1052623499354989     Document Type: Article

References (10)

1. A. CONN, K. SCHEINBERG, AND P. L. TOINT, On the convergence of derivative-free methods for unconstrained optimization, in Approximation Theory and Optimization, M. D. Buhmann and A. Iserles, eds., Cambridge University Press, Cambridge, 1997, pp. 83-108.
2. I. D. COOPE AND C. J. PRICE, A direct search conjugate directions algorithm for unconstrained minimization, ANZIAM J., 42(E) 2000, pp. C478-498.
3. C. DAVIS, Theory of positive linear dependence, Amer. J. Math., 76 (1954), pp. 733-746.
4. C. ELSTER AND A. NEUMAIER, A grid algorithm for bound-constrained optimization of noisy functions, IMA J. Numer. Anal., 15 (1995), pp. 585-608.
5. R. HOOKE AND T. A. JEEVES, Direct search solution of numerical and statistical problems, J. Assoc. Comput. Mach., 8 (1961), pp. 212-219.
6. R. M. LEWIS AND V. TORCZON, Rank ordering and positive bases in pattern search algorithms, Math. Program., to appear.
7. M. J. D. POWELL, Direct search algorithms for optimization calculations, Acta Numer., 7 (1998), pp. 287-336.
8. V. TORCZON, On the convergence of the multidirectional search algorithm, SIAM J. Optim., 1 (1991), pp. 123-145.
9. V. TORCZON, On the convergence of pattern search algorithms, SIAM J. Optim., 7 (1997), pp. 1-25.
10. M. H. WRIGHT, Direct search methods: Once scorned now respectable, in Proceedings of the 1995 Dundee Biennial Conference in Numerical Analysis, Longman, Harlow, UK, 1996, pp. 191-208.