Pattern search methods for user-provided points: Application to molecular geometry problems

SIAM Journal on Optimization

Volumn 14, Issue 4, 2004, Pages 1216-1236

  Alberto, Pedro ^a,b   Nogueira, Fernando ^a,b   Rocha, Humberto ^c   Vicente, Luís N ^d  

^a UNIVERSITY OF COIMBRA   (Portugal)

^b Ctro de Fis Computacional   (Portugal)

^c Portuguese Catholic University Viseu   (Portugal)

^d UNIVERSITY OF COIMBRA   (Portugal)

Author keywords

Expensive function evaluations; Geometrical transformations; Molecular geometry; Parallel computing; Pattern search methods; User provided points

Indexed keywords

EXPENSIVE FUNCTION EVALUATIONS; GEOMETRICAL TRANSFORMATIONS; MOLECULAR GEOMETRY; PATTERN SEARCH METHODS; USER-PROVIDED POINTS;

ATOMS; COMPUTATIONAL GEOMETRY; FUNCTIONS; MATHEMATICAL TRANSFORMATIONS; MOLECULAR PHYSICS; MOLECULES; PARALLEL PROCESSING SYSTEMS; PROBLEM SOLVING;

PATTERN MATCHING;

EID: 9944263116     PISSN: 10526234     EISSN: None     Source Type: Journal    
DOI: 10.1137/S1052623400377955     Document Type: Article

References (34)

1. P. ALBERTO, F. NOGUEIRA, H. ROCHA, AND L. N. VICENTE, Pattern search methods for user-provided points, in Computational Science - IOCS 2001, Lecture Notes in Comput. Sci. 2074, V. N. Alexandrov, J. J. Dongarra, B. A. Juliano, R. S. Renner, and C. J. Kenneth Tan, eds., Springer-Verlag, Berlin, 2001, pp. 95-98.
2. C. AUDET AND J. E. DENNIS, JR., Pattern search algorithms for mixed variable programming, SIAM J. Optim., 11 (2000), pp. 573-594.
3. R. BISWAS AND D. R. HAMANN, Simulated annealing of silicon atom clusters in Langevin molecular dynamics, Phys. Rev. B, 34 (1986), pp. 895-901.
4. M. BORN AND K. HUANG, Dynamical Theory of Crystal Lattices, Clarendon Press, Oxford, 1954.
5. G. E. P. Box, Evolutionary operation: A method for increasing industrial productivity, Appl. Statist., 6 (1957), pp. 81-101.
6. R. CAR AND M. PARRINELLO, Unified approach for molecular dynamics and density-functional techniques, Phys. Rev. Lett., 55 (1985), pp. 2471-2474.
7. D.M. CEPERLEY AND B. J. ALDER, Ground state of the electron gas by a stochastic method, Phys. Rev. Lett., 45 (1980), pp. 566-569.
8. A. R. CONN, K. SCHEINBERG, AND P. L. TOINT, Recent progress in unconstrained nonlinear optimization without derivatives, Math. Programming, 79 (1997), pp. 397-414.
9. C. DAVIS, Theory of positive linear dependence, Amer. J. Math., 76 (1954), pp. 733-746.
10. J. E. DENNIS, JR., AND V. TORCZON, Direct search methods on parallel machines, SIAM J. Optim., 1 (1991), pp. 448-474.
11. G. H. GOLUB AND C. F. VAN LOAN, Matrix Computations, 3rd ed., The John Hopkins University Press, Baltimore, MD, 1996.
12. W. E. HART, A generalized stationary point convergence theory for evolutionary algorithms, in Proceedings of the 7th International Conference on Genetic Algorithms, East Lansing, MI, 1997, Thomas Back, ed., Morgan Kaufmann, San Francisco, 1997, pp. 127-134.
13. W. E. HART, Comparing evolutionary programs and evolutionary pattern search algorithms: A drug docking application, in Proceedings of the Genetic and Evolutionary Computation Conference, Orlando, FL, 1999, Morgan Kaufmann, San Francisco, 1999, pp. 855-862.
14. M. R. HOARE AND J. A. MCINNES, Morphology and statistical statics of simple microclusters, Adv. Phys., 32 (1983), pp. 791-821.
15. P. HOHENBERG AND W. KOHN, Inhomogeneous electron gas, Phys. Rev. B, 136 (1964), pp. 864-871.
16. R. HOOKE AND T. A. JEEVES, "Direct search" solution of numerical and statistical problems, J. ACM, 8 (1961), pp. 212-229.
17. J. IHM, Total energy calculations in solid state physics, Rep. Prog. Phys., 51 (1988), pp. 105-142.
18. J. IHM, A. ZUNGER, AND M. L. COHEN, Momentum-space formalism for the total energy of solids, J. Phys. C: Solid State Phys., 12 (1979), pp. 4409-4422; Errata, J. Phys. C: Solid State Phys., 13 (1980), p. 3095.
19. J. IHM, A. ZUNGER, AND M. L. COHEN, Momentum-space formalism for the total energy of solids, J. Phys. C: Solid State Phys., 12 (1979), pp. 4409-4422; Errata, J. Phys. C: Solid State Phys., 13 (1980), p. 3095.
20. W. KOHN AND L. J. SHAM, Self-consistent equations including exchange and correlation effects, Phys. Rev. A, 140 (1965), pp. 1133-1138.
21. R. M. LEWIS AND V. TORCZON, Rank Ordering and Positive Bases in Pattern Search Algorithms, Technical report TR96-71, ICASE, NASA Langley Research Center, Hampton, VA, 1999.
22. R. M. LEWIS, V. TORCZON, AND M. W. TROSSET, Why pattern search works, OPTIMA, MPS Newsletter, 59 (1998), pp. 1-7.
23. J. C. MEZA AND M. L. MARTINEZ, On the use of direct search methods for the molecular conformation problem, J. Comput. Chem., 15 (1994), pp. 627-632.
24. J. A. NELDER AND R. MEAD, A simplex method for function minimization, Comput. J., 7 (1965), pp. 308-313.
25. J. P. PERDEW AND Y. WANG, Accurate and simple analytic representation of the electron-gas correlation energy, Phys. Rev. B, 45 (1992), pp. 13244-13249.
26. J. P. PERDEW AND A. ZUNGER, Self-interaction correction to density-functional approximations for many-electron systems, Phys. Rev. B, 23 (1981), pp. 5048-5079.
27. W. E. PICKETT, Pseudopotential methods in condensed matter applications, Comp. Phys. Rep., 9 (1989), pp. 115-198.
28. M. J. D. POWELL, Direct search algorithms for optimization calculations, in Acta Numer. 7, Cambridge University Press, Cambridge, UK, 1998, pp. 287-336.
29. V. TORCZON, On the convergence of the multidirectional search algorithm, SIAM J. Optim., 1 (1991), pp. 123-145.
30. V. TORCZON, On the convergence of pattern search algorithms, SIAM J. Optim., 7 (1997), pp. 1-25.
31. M. W. TROSSET, I know it when I see it: Toward a definition of direct search methods, SIAG/OPT Views-and-News, 9 (1997), pp. 7-10.
32. N. TROULLIER AND J. L. MARTINS, Efficient pseudopotentials for plane-wave calculations, Phys. Rev. B, 43 (1991), pp. 1993-2006.
33. M. H. WRIGHT, Direct search methods: Once scorned, now respectable, in Numerical Analysis 1995 (Proceedings of the 1995 Dundee Biennial Conference in Numerical Analysis), Pitman Res. Notes Math. Ser. 344, D. F. Griffiths and G. A. Watson, eds., CRC Press, Boca Raton, FL, 1996, pp. 191-208.
34. W. ZHONG, G. OVERNEY, AND D. TOMÁNEK, Structural properties of Fe crystals, Phys. Rev. B, 47 (1993), pp. 95-99.