BB: An R package for solving a large system of nonlinear equations and for optimizing a high-dimensional nonlinear objective function

Journal of Statistical Software

Volumn 32, Issue 4, 2009, Pages 1-26

  Varadhan, Ravi ^a   Gilbert, Paul D ^b  

^a JOHNS HOPKINS UNIVERSITY SCHOOL OF MEDICINE   (United States)

^b BANK OF CANADA   (Canada)

Author keywords

Accelerate failure time model; Barzilai Borwein; Derivative free; Estimating equations; Large scale optimization; Non monotone line search; Non smooth optimization; Rank based regression

Indexed keywords

EID: 70350426511     PISSN: 15487660     EISSN: 15487660     Source Type: Journal    
DOI: 10.18637/jss.v032.i04     Document Type: Article

References (26)

1. Barzilai J, Borwein JM (1988). "Two-Point Step Size Gradient Methods." IMA Journal of Numerical Analysis, 8(1), 141-148.
2. Birgin EG, Martínez JM, Raydan M (2001). "Algorithm 813: SPG-Software for Convex- Constrained Optimization." ACM Transactions on Mathematical Software, 27(3), 340-349.
3. Carroll RJ, Ruppert D (1988). Transformation and Weighting in Regression. Chapman & Hall/CRC Press, London, UK.
4. Dennis JE, Schnabel RB (1983). Numerical Methods for Unconstrained Optimization and Nonlinear Equations. Prentice-Hall, Englewood Cliffs, New Jersey.
5. Dickson ER, Grambsch PM, Fleming TR, Fisher LD, Langworthy A (1989). "Prognosis in Primary Biliary Cirrhosis: Model for Decision Making." Hepatology, 10, 1-7.
6. Diggle P, Heagerty P, Liang KY, Zeger SL (2002). The Analysis of Longitudinal Data. Oxford University Press, New York.
7. Fletcher R (2001). "On the Barzilai-Borwein Method." Technical Report NA/207, University of Dundee, Dundee, Scotland. URL http://www.maths.dundee.ac.uk/~fletcher/.
8. Grippo L, Lampariello F, Lucidi S (1986). "A Nonmonotone Line Search Technique for Newton's Method." SIAM Journal on Numerical Analysis, 23, 707-16.
9. Hasselman B (2009). nleqslv: Solve Systems of Non Linear Equations. R package version 1.4, URL http://CRAN.R-project.org/package=nleqslv.
10. Jin Z, Lin DY, Wei LJ, Ying Z (2003). "Rank-Based Inference for the Accelerated Failure Time Model." Biometrika, 90, 341-353.
11. Kalbfleisch JD, Prentice RL (2002). The Statistical Analysis of Failure Time Data. John Wiley & Sons, Hoboken, NJ.
12. Kearfoot RB (1987). "Some Tests of Generalized Bisection." ACM Transactions on Mathematical Software, 13(3), 197-220.
13. La Cruz W, Martínez JM, Raydan M (2006). "Spectral Residual Method Without Gradient Information for Solving Large-Scale Nonlinear Systems of Equations." Mathematics of Computation, 75(255), 1429.
14. La Cruz W, Raydan M (2003). "Nonmonotone Spectral Methods for Large-Scale Nonlinear Systems." Optimization Methods and Software, 18(5), 583-599.
15. Lin DY, Geyer CJ (1992). "Computational Methods for Semiparametric Linear Regression with Censored Data." Journal of Computational and Graphical Statistics, 1(1), 77-90.
16. Luengo F, Raydan M (2003). "Gradient Method with Dynamical Retards for Large-Scale Optimization Problems." Electronic Transactions on Numerical Analysis, 16, 186-193.
17. Luksan L, Vlcek J (2003). "Test Problems for Unconstrained Optimization." Technical report, Academy of Sciences of the Czech Republic, Institute of Computer Science. URL http://www.cs.cas.cz/luksan/reports.html.
18. Nelder JA, Mead R (1965). "A Simplex Method for Function Minimization." Computer Journal, 7, 308.
19. Ortega JM, Rheinboldt WC (1970). Iterative Solution of Non-Linear Equations in Several Variables. Academic Press, New York.
20. Raydan M (1997). "The Barzilai and Borwein Gradient Method for the Large Scale Unconstrained Minimization Problem." SIAM Journal of Optimization, 7, 26-33.
21. Raydan M (2009). "Marcos Raydan's Home Page." URL http://kuainasi.ciens.ucv.ve/ccct/mraydan/mraydan_pub.html.
22. R Development Core Team (2009). R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria. ISBN 3-900051-07-0, URL http://www.R-project.org/.
23. Small CG, Wang J (2003). Numerical Methods for Nonlinear Estimating Equations. Oxford University Press, New York.
24. Therneau T, Lumley T (2009). survival: Survival Analysis, Including Penalised Likelihood. R package version 2.35-4, URL http://CRAN.R-project.org/package=survival.
25. Varadhan R, Roland C (2008)."Simple and Globally Convergent Methods for Accelerating the Convergence of Any EM Algorithm." Scandinavian Journal of Statistics, 35(2), 335-353.
26. Zeileis A (2005). "CRAN Task Views." R News, 5(1), 39-40. URL http://CRAN.R-project. org/doc/Rnews/.