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Infinite Linear Programming

In: Infinite Matrices and Their Recent Applications

Author

Listed:
  • P. N. Shivakumar

    (University of Manitoba, Department of Mathematics)

  • K. C. Sivakumar

    (Indian Institute of Technology, Madras, Department of Mathematics)

  • Yang Zhang

    (University of Manitoba, Department of Mathematics)

Abstract

Infinite linear programming problems are linear optimization problems where, in general, there are infinitely (possibly uncountably) many variables and constraints related linearly. There are many problems arising from real world situations that can be modelled as infinite linear programs. These include the bottleneck problem of Bellman in economics, infinite games, and continuous network flows, to name a few. We refer to the excellent book by Anderson and Nash [2] for an exposition of infinite linear programs, a simplex type method of solution and applications. Semi-infinite linear programs are a subclass of infinite programs, wherein the number of variables is finite with infinitely many constraints in the form of equations or inequalities. Semi-infinite programs have been shown to have applications in a number of areas that include robot trajectory planning, eigenvalue computations, vibrating membrane problems, and statistical design problems. For more details we refer to the two excellent reviews by Hettich and Kortanek [43] and Polak [90] on semi-infinite programming.

Suggested Citation

  • P. N. Shivakumar & K. C. Sivakumar & Yang Zhang, 2016. "Infinite Linear Programming," Springer Books, in: Infinite Matrices and Their Recent Applications, chapter 0, pages 87-92, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-30180-8_7
    DOI: 10.1007/978-3-319-30180-8_7
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