Detection and remediation of stagnation in the Nelder-Mead algorithm using a sufficient decrease condition

SIAM Journal on Optimization

Volumn 10, Issue 1, 1999, Pages 43-55

  Kelley, C T ^a  

^a NORTH CAROLINA STATE UNIVERSITY   (United States)

Author keywords

Nelder Mead algorithm; Stagnation; Sufficient decrease

Indexed keywords

EID: 0033274347     PISSN: 10526234     EISSN: None     Source Type: Journal    
DOI: 10.1137/S1052623497315203     Document Type: Article

References (27)

1. L. ARMIJO, Minimization of functions having Lipschitz-continuous first partial derivatives, Pacific J. Math., 16 (1966), pp. 1-3.
2. K. R. BAILEY AND B. G. FITZPATRICK, Estimation of Groundwater Flow Parameters Using Least Squares, Tech. Report CRSC-TR96-13, Center for Research in Scientific Computation, North Carolina State University, Raleigh, April 1996.
3. K. R. BAILEY, B. G. FITZPATRICK, AND M. A. JEFFRIES, Least Squares Estimation of Hydraulic Conductivity from Field Data, Tech. Report CRSC-TR95-8, Center for Research in Scientific Computation, North Carolina State University, Raleigh, February 1995.
4. D. M. BORTZ AND C. T. KELLEY, The simplex gradient and noisy optimization problems, in Computational Methods for Optimal Design and Control, Progr. System Control Theory 24, Birkhäuser, Boston, MA, 1998, p. 77-90.
5. A. G. BUCKLEY AND H. MA, A Derivative-Free Algorithm for Parallel and Sequential Optimization, Tech. Report, Computer Science Department, University of Victoria, BC, Canada, October 1994.
6. J. W. DAVID, C. T. KELLEY, AND C. Y. CHENG, Use of an Implicit Filtering Algorithm for Mechanical System Parameter Identification, SAE Paper 960358, Society of Automotive Engineers International Congress and Exposition Conference Proceedings, Model. CI and SI Engines, Detroit, MI, 1996, pp. 189-194.
7. J. E. DENNIS AND R. B. SCHNABEL. Numerical Methods for Unconstrained Optimization and Nonlinear Equations, Classics Appl. Math. 16, SIAM, Philadelphia, 1996.
8. J. E. DENNIS, JR., AND V. TORCZON, Direct search methods on parallel machines, SIAM J. Optim., 1 (1991), pp. 448-474.
9. J. E. DENNIS AND D. J. WOODS, Optimization on microcomputers: The Nelder-Mead simplex algorithm, in New Computer Environments: Microcomputers in Large-Scale Computing, A. Wouk, ed., Proc. Appl. Math. 27, SIAM, Philadelphia, 1987, pp. 116-122.
10. P. GILMORE AND C. T. KELLEY, An implicit filtering algorithm for optimization of functions with many local minima, SIAM J. Optim., 5 (1995), pp. 269-285.
11. R. HOOKE AND T. A. JEEVES, "Direct search" solution of numerical and statistical problems, J. Assoc. Comput. Mach., 8 (1961), pp. 212-229.
12. C. T. KELLEY, Iterative Methods for Linear and Nonlinear Equations, Frontiers Appl. Math. 16, SIAM, Philadelphia, 1995.
13. C. T. KELLEY, Iterative Methods for Optimization, Frontiers Appl. Math. 18, SIAM, Philadelphia, 1999.
14. J. C. LAGARIAS, J. A. REEDS, M. H. WRIGHT, AND P. E. WRIGHT, Convergence properties of the Nelder-Mead simplex algorithm in low dimensions, SIAM J. Optim., 9 (1999), pp. 112-147.
15. K. I. M. MCKINNON, Convergence of the Nelder-Mead simplex method to a nonstationary point, SIAM J. Optim., 9 (1999), pp. 148-158.
16. J. A. NELDER AND R. MEAD, A simplex method for function minimization, Comput. J., 7 (1965), pp. 308-313.
17. J. M. ORTEGA AND W. C. RHEINBOLDT, Iterative Solution of Nonlinear Equations in Several Variables, Academic Press, New York, 1970.
18. D. STONEKING, G. BILBRO, R. TREW, P. GILMORE, AND C. T. KELLEY, Yield optimization using a GaAs process simulator coupled to a physical device model, IEEE Trans. Microwave Theory and Techniques, 40 (1992), pp. 1353-1363.
19. D. E. STONEKING, G. L. BILBRO, R. J. TREW, P. GILMORE, AND C. T. KELLEY, Yield optimization using a GaAs process simulator coupled to a physical device model, in Proceedings, IEEE/Cornell Conference on Advanced Concepts in High Speed Devices and Circuits, IEEE, Piscataway, NJ, 1991, pp. 374-383.
20. V. TORCZON, On the convergence of the multidirectional search algorithm, SIAM J. Optim., 1 (1991), pp. 123-145.
21. V. TORCZON, On the convergence of pattern search algorithms, SIAM J. Optim., 7 (1997), pp. 1-25.
22. P. TSENG, Fortified-Descent Simplicial Search Method: A General Approach, Tech. Report, Department of Mathematics, University of Washington, Seattle, WA, 1995.
23. T. A. WINSLOW, R. J. TREW, P. GILMORE, AND C. T. KELLEY, Doping profiles for optimum class B performance of GaAs mesfet amplifiers, in Proceedings, IEEE/Cornell Conference on Advanced Concepts in High Speed Devices and Circuits, IEEE, Piscataway, NJ, 1991, pp. 188-197.
24. T. A. WINSLOW, R. J. TREW, P. GILMORE, AND C. T. KELLEY, Simulated performance optimization of GaAs MESFET amplifiers, in Proceedings IEEE/Cornell Conference on Advanced Concepts in High Speed Devices and Circuits, IEEE, Piscataway, NJ, 1991, pp. 393-402.
25. D. J. WOODS, An Interactive Approach for Solving Multi-Objective Optimization Problems, Ph.D. thesis, Rice University, Houston, TX, 1985.
26. M. H. WRIGHT, Direct search methods: Once scorned, now respectable, in Numer. Anal. 1995, Proceedings of the 1995 Dundee Bienneal Conference in Numerical Analysis, D. F. Griffiths and G. A. Watson, eds., Pitman Res. Notes Math. Ser. 344, Longman, Harlow, UK, 1996, pp. 191-208.
27. S. K. ZAVRIEV, On the global optimization properties of finite-difference local descent algorithms, J. Global Optim., 3 (1993), pp. 67-78.