Grid restrained Nelder-Mead algorithm

Computational Optimization and Applications

Volumn 34, Issue 3, 2006, Pages 359-375

  Bűrmen, Árpád ^a   Puhan, Janez ^a   Tuma, Tadej ^a  

^a UNIVERSITY OF LJUBLJANA   (Slovenia)

Author keywords

Direct search; Grid; Nelder Mead algorithm; Simplex; Unconstrained minimization

Indexed keywords

ALGORITHMS; NUMERICAL METHODS; OPTIMIZATION; PROBLEM SOLVING;

DIRECT SEARCH; GRID; NELDER-MEAD ALGORITHMS; SIMPLEX; UNCONSTRAINED MINIMIZATION;

COMPUTATION THEORY;

EID: 33745712168     PISSN: 09266003     EISSN: 15732894     Source Type: Journal    
DOI: 10.1007/s10589-005-3912-z     Document Type: Article

References (17)

1. D. Byatt, "A convergent variant of the Nelder-Mead algorithm," Master's thesis, Mathematics and Statistics Department, University of Canterbury, Christchurch, NZ, 2000.
2. I.D. Coope and C. J. Price, "Frame based methods for unconstrained optimization," Journal of Optimization Theory and Applications, vol. 107, pp. 261-274, 2000.
3. I.D. Coope and C.J. Price, "On the convergence of grid-based methods for unconstrained optimization," SIAM J. Optim., vol. 11, pp. 859-869, 2001.
4. C. Davis, "Theory of positive linear dependence," American Journal of Mathematics, vol. 76, pp. 733-746, 1954.
5. C.T. Kelley, "Detection and remediation of stagnation in the Nelder-Mead algorithm using a sufficient decrease condition," SIAM Journal on Optimization, vol. 10, pp. 43-55, 1999.
6. J.C. Lagarias, "Convergence properties of the Nelder-Mead simplex method in low dimensions," SIAM Journal on Optimization, vol. 9, pp. 112-147, 1998.
7. R.M. Lewis and V.J. Torczon, "Rank ordering and positive bases in pattern search algorithms," ICASE NASA Langley Research Center, Hampton, VA 23681-0001, USA, Tech. Report 96-71, 1996.
8. R.M. Lewis, V.J. Torczon, and M.W. Trosset, "Direct search methods: Then and now," Journal of Computational and Applied Mathematics, vol. 124, pp. 191-207, 2000.
9. K.I.M. McKinnon, "Convergence of the Nelder-Mead simplex method," SIAM Journal on Optimization, vol. 9, pp. 148-158, 1998.
10. J.J. More, B.S. Garbow, and K.E. Hillstrom, "Testing unconstrained optimization software," ACM Transactions on Mathematical Software, vol. 7, pp. 17-41, 1981.
11. J.A. Nelder and R. Mead, "A simplex method for function minimization," The Computer Journal, vol. 7, pp. 308-313, 1965.
12. C.J. Price, I.D. Coope, and D. Byatt, "A convergent variant of the Nelder-Mead algorithm," Journal of Optimization Theory and Applications, vol. 113, pp. 5-19, 2002.
13. A.S. Rykov, "Simplex algorithms for unconstrained minimization," Problems of Control and Information Theory, vol. 12, pp. 195-208, 1983.
14. V.J. Torczon, "Multi-directional search: A direct search algorithm for parallel machines," PhD thesis, Department of Mathematical Sciences, Rice University, Houston, TX 77251-1892, USA, 1989.
15. V.J. Torczon, "On the convergence of pattern search methods," SIAM J. Optim., vol. 7, pp. 1-25, 1997.
16. P. Tseng, "Fortified-descent simplical search method: A general approach," SIAM Journal on Optimization, vol. 10, pp. 269-288, 1999.
17. M.H. Wright, "Direct search methods: Once scorned, now respectable," in Proceedings of the 1995 Dundee Biennial Conference in Numerical Analysis, Dundee, UK, 1996, pp. 191-208.