Skip to main content
SpringerLink
Log in

Factorable programming

  • Reference work entry
  • First Online:
Encyclopedia of Operations Research and Management Science

  • 54 Accesses

Factorable programming problems are mathematical programming problems of the form

for i = 1,..., m, in which all the functions involved are factorable. Loosely, a factorable function is a multivariate function that can be written as the last of a finite sequence of functions, in which the first n functions in the sequence are just the coordinate variables, and each function beyond the nth is a sum, a product, or a single-variable transformation of previous functions in the sequence. More rigorously, let [f 1(x),f 2(x),...,f L(x)] be a finite sequence of functions such that f i: R n → R where each f i(x) is defined according to one of the following rules:

  • Rule 1: For i = 1,..., n,f i(x) is defined to be the ith Euclidean coordinate, or f i(x) = x i.

  • Rule 2: For i = n + 1,..., L, f 1(x) is formed using one of the following compositions:

  1. a)

    f i(x) = f j(i)(x) + f k(i)(x); or

  2. b)

    f i(x) = f j(i)(x) ⋅ f k(i)(x); or

  3. c)

    f i(x) = T i[f j(i)(x)];

where j(i) < i, k(i) < i, and T iis a function...

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 532.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. DeSilva, A. and McCormick, G.P. (1978). “Sensitivity Analysis in Nonlinear Programming Using Factorable Symbolic Input,” Technical Report T-365, The George Washington University, Institute for Management Science and Engineering, Washington, DC.

    Google Scholar 

  2. Emami, G. (1978). “Evaluating Strategies for Newton's Method Using a Numerically Stable Generalized Inverse Algorithm,” Dissertation, Department of Operations Research, George Washington University, Washington, DC.

    Google Scholar 

  3. Falk, J.E. (1973). “Global Solutions of Signomial Problems,” Technical report T-274, George Washington University, Department of Operations Research, Washington, DC.

    Google Scholar 

  4. Falk, J.E. and Soland, R.M. (1969). “An Algorithm for Separable Nonconvex Programming Problems,” Management Science, 15, 550–569.

    Google Scholar 

  5. Fiacco, A.V. and McCormick, G.P. (1968). Nonlinear Programming: Sequential Unconstrained Minimization Techniques, John Wiley, New York.

    Google Scholar 

  6. Ghaemi, A. and McCormick, G.P. (1979). “Factorable Symbolic SUMT: What Is It? How Is It Used?,” Technical Report No. T-402, Institute for Management Science and Engineering, George Washington University, Washington, DC.

    Google Scholar 

  7. Ghotb, F. (1980). “Evaluating Strategies for Newton's Method for Linearly Constrained Optimization Problems,” Dissertation, Department of Operations Research, George Washington University, Washington, DC.

    Google Scholar 

  8. Hoffman, K.L. (1975). “NUGLOBAL-User Guide,” Technical Report TM-64866, Department of Operations Research, George Washington University, Washington, DC.

    Google Scholar 

  9. Jackson, R.H. F. and McCormick, G.P. (1986). “The Polyadic Structure of Factorable Function Tensors with Applications to High-order Minimization Techniques,” JOTA, 51, 63–94.

    Google Scholar 

  10. Jackson, R.H. F. and McCormick, G.P. (1988). “Second-order Sensitivity Analysis in Factorable Programming: Theory and Applications,” Mathematical Programming, 41, 1–27.

    Google Scholar 

  11. Jackson, R.H. F., McCormick, G.P., and Sofer, A. (1989). “FACTUNC, A User-friendly System for Optimization,” Technical Report NISTIR 89-4159, National Institute of Standards and Technology, Gaithersburg, Maryland.

    Google Scholar 

  12. Kedem, G. (1980). “Automatic Differentiation of Computer Programs,” ACM Transactions on Mathematical Software, 6, 150–165.

    Google Scholar 

  13. Leaver, S.G. (1984). “Computing Global Maximum Likelihood Parameter Estimates for Product Models for Frequency Tables Involving Indirect Observation,” Dissertation, The George Washington University, Department of Operations Research, Washington, DC.

    Google Scholar 

  14. McCormick, G.P. (1974). “A Minimanual for Use of the SUMT Computer Program and the Factorable Programming Language,” Technical Report SOL 74-15, Department of Operations Research, Stanford University, Stanford, California.

    Google Scholar 

  15. McCormick, G.P. (1976). “Computability of Global Solutions to Factorable Nonconvex Programs: Part I–Convex Underestimating Problems,” Mathematical Programming, 10, 147–145.

    Google Scholar 

  16. McCormick, G.P. (1983). Nonlinear Programming: Theory, Algorithms and Applications, John Wiley, New York.

    Google Scholar 

  17. McCormick, G.P. (1985). “Global Solutions to Factorable Nonlinear Optimization Problems Using Separable Programming Techniques,” Technical Report NBSIR 85-3206, National Bureau of Standards, Gaithersburg, Maryland.

    Google Scholar 

  18. Miele, A. and Gonzalez, S. (1978). “On the Comparative Evaluation of Algorithms for Mathematical Programming Problems,” Nonlinear Programming, 3, edited by O.L. Mangasarian et al., Academic Press, New York, 337–359.

    Google Scholar 

  19. Mylander, W.C., Holmes, R., and McCormick, G.P. (1971). “A Guide to SUMT-Version 4: The Computer Program Implementing the Sequential Unconstrained Minimization Technique for Nonlinear Programming,” Technical Report RAC-P-63, Research Analysis Corporation, McLean, Virginia.

    Google Scholar 

  20. Pugh, R.E. (1972). “A Language for Nonlinear Programming Problems,” Mathematical Programming, 2, 176–206.

    Google Scholar 

  21. Rall, L.B. (1980). “Applications of Software for Automatic Differentiation in Numerical Computations,” Computing, Supplement, 2, 141–156.

    Google Scholar 

  22. Reiter, A. and Gray, J.H. (1967). “Compiler for Differentiable Expressions (CODEX) for the CDC 3600,” MRC Technical Report No. 791, University of Wisconsin, Madison, Wisconsin.

    Google Scholar 

  23. Shayan, M.E. (1978). “A Methodology for Comparing Algorithms and a Method for Computing mth Order Directional Derivatives Based on Factorable Programming,” Dissertation, Department of Operations Research, George Washington University, Washington, DC.

    Google Scholar 

  24. Sofer, A. (1983). “Computationally Efficient Techniques for Generalized Inversion,” Dissertation, Department of Operations Research, The George Washington University, Washington, DC.

    Google Scholar 

  25. Warner, D.D. (1975). “A Partial Derivative Generator,” Computing Science Technical Report No. 28, Bell Telephone Laboratories, Murray Hill, New Jersey.

    Google Scholar 

  26. Wengert, R.E. (1964). “A Simple Automatic Derivative Evaluation Program,” Communications of the ACM, 7, 463–464.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. National Institute of Standards and Technology, Gaithersburg, Maryland, USA

    Richard H. F. Jackson

Authors
  1. Richard H. F. Jackson
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Robert H. Smith School of Business, University of Maryland, College Part, Maryland, USA

    Saul I. Gass

  2. School of Information Technology & Engineering, George Mason University, Fairfax, Virginia, USA

    Carl M. Harris

Rights and permissions

Reprints and permissions

Copyright information

© 2001 Kluwer Academic Publishers

About this entry

Cite this entry

Jackson, R.H.F. (2001). Factorable programming . In: Gass, S.I., Harris, C.M. (eds) Encyclopedia of Operations Research and Management Science. Springer, New York, NY. https://doi.org/10.1007/1-4020-0611-X_328

Download citation

  • DOI: https://doi.org/10.1007/1-4020-0611-X_328

  • Published:

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-0-7923-7827-3

  • Online ISBN: 978-1-4020-0611-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation