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Interior Point Methods for Linear Programming: Just Call Newton, Lagrange, and Fiacco and McCormick!

Author

Listed:
  • Roy Marsten

    (School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, GA 30332)

  • Radhika Subramanian

    (School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, GA 30332)

  • Matthew Saltzman

    (Department of Mathematical Sciences, Clemson University, Clemson, SC 29631)

  • Irvin Lustig

    (Department of Civil Engineering and Operations Research, Princeton University, Princeton, NJ 08544)

  • David Shanno

    (RUTCOR, Rutgers University, New Brunswick, NJ 08903)

Abstract

Interior point methods are the right way to solve large linear programs. They are also much easier to derive, motivate, and understand than they at first appeared. Lagrange told us how to convert a minimization with equality constraints into an unconstrained minimization. Fiacco and McCormick told us how to convert a minimization with inequality constraints into a sequence of unconstrained minimizations. Newton told us how to solve unconstrained minimizations. Linear programs are minimizations with equations and inequalities. Voila!

Suggested Citation

  • Roy Marsten & Radhika Subramanian & Matthew Saltzman & Irvin Lustig & David Shanno, 1990. "Interior Point Methods for Linear Programming: Just Call Newton, Lagrange, and Fiacco and McCormick!," Interfaces, INFORMS, vol. 20(4), pages 105-116, August.
    • Handle: RePEc:inm:orinte:v:20:y:1990:i:4:p:105-116
    DOI: 10.1287/inte.20.4.105
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    Cited by:

    1. Richard D. McBride & John W. Mamer, 2004. "Implementing an LU Factorization for the Embedded Network Simplex Algorithm," INFORMS Journal on Computing, INFORMS, vol. 16(2), pages 109-119, May.
    2. Kraft, Edwin R., 2002. "Scheduling railway freight delivery appointments using a bid price approach," Transportation Research Part A: Policy and Practice, Elsevier, vol. 36(2), pages 145-165, February.
    3. M. Xiong & J. Wang & P. Wang, 2002. "Differential-Algebraic Approach to Linear Programming," Journal of Optimization Theory and Applications, Springer, vol. 114(2), pages 443-470, August.
    4. G. Y. Zhao, 1999. "Interior-Point Methods with Decomposition for Solving Large-Scale Linear Programs," Journal of Optimization Theory and Applications, Springer, vol. 102(1), pages 169-192, July.
    5. Alexandra M. Newman & Martin Weiss, 2013. "A Survey of Linear and Mixed-Integer Optimization Tutorials," INFORMS Transactions on Education, INFORMS, vol. 14(1), pages 26-38, September.
    6. Torres-Rojo, J. M., 2001. "Risk management in the design of a feeding ration: a portfolio theory approach," Agricultural Systems, Elsevier, vol. 68(1), pages 1-20, April.
    7. Gondzio, Jacek, 2012. "Interior point methods 25 years later," European Journal of Operational Research, Elsevier, vol. 218(3), pages 587-601.
    8. John W. Mamer & Richard D. McBride, 2000. "A Decomposition-Based Pricing Procedure for Large-Scale Linear Programs: An Application to the Linear Multicommodity Flow Problem," Management Science, INFORMS, vol. 46(5), pages 693-709, May.

    More about this item

    Keywords

    programming: linear; tutorial;

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