Linear Programming

  • Urmila M. Diwekar
Part of the Applied Optimization book series (APOP, volume 80)


Linear programming (LP) problems involve a linear objective function and linear constraints, as shown below in Example 2.1


Feasible Region Simplex Method Shadow Price Interior Point Method Slack Variable 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Arbel A. (1993), Exploring Interior-Point Linear Programming Algorithms and Software, MIT Press, Cambridge, MA.zbMATHGoogle Scholar
  2. 2.
    Carter M. W. and C. C. Price (2001), Operations Research: A Practical Introduction, CRC Press, New York, NY.Google Scholar
  3. 3.
    Dantzig G. B.(1963), Linear Programming and Extensions, Princeton University Press, NJ.zbMATHGoogle Scholar
  4. 4.
    Dantzig G. B. and Thapa M. N. (1996), Linear Programming, SpringerVerlag, New York.Google Scholar
  5. 5.
    Emmett A. (1985), Karmarkar’s algorithm: a threat to simplex, IEEE Spectrum, December, 54.Google Scholar
  6. 6.
    Fiacco A. V. and McCormick G. P. (1968), Nonlinear Programming: Sequential Unconstrained Minimization, John Wiley and Sons, New York, NY (reprinted by SIAM Publications, 1990).zbMATHGoogle Scholar
  7. 7.
    Narayan, V., Diwekar U.M. and Hoza M. (1996), Synthesizing optimal waste blends, Industrial and Engineering Chemistry Research, 35, 3519.CrossRefGoogle Scholar
  8. 8.
    Nocedal J. and S. Wright (1999), Numerical Optimization, Springer Series in Oerations Research, Springer-Verlag, New York, NY.zbMATHCrossRefGoogle Scholar
  9. 9.
    Taha H. A. (1997), Operations Research: An Introduction, Sixth Edition, Prentice Hall , Upper Saddle River, NJ.zbMATHGoogle Scholar
  10. 10.
    Winston W. L. (1991), Operations Research: Applications and Algorithms, Second Edition, PWS-KENT Co., Boston, MA.zbMATHGoogle Scholar
  11. 11.
    Wright S. J. (1997), Primal-Dual Interior-Point Methods, SIAM Publications, Philadelphia, PA.zbMATHCrossRefGoogle Scholar
  12. 12.
    Wright S. J. (1999), Algorithms and software for linear and nonlinear programming, Foundations of Computer Aided Process’99, Paper I07, CACHE Corporation, AIChE, New York, NY.Google Scholar

Copyright information

© Springer Science+Business Media New York 2003

Authors and Affiliations

  • Urmila M. Diwekar
    • 1
  1. 1.Center for Uncertain Systems: Tools for Optimization & Management, Department of Chemical Engineering, and Institute for Environmental Science & PolicyUniversity of Illinois at ChicagoChicagoUSA

Personalised recommendations