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Separably-infinite programs

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Summary

Separably-infinite programs are a class of linear infinite programs that are related to semi-infinite programs and which have applications in economics and statistics. These programs have an infinite number of variables and an infinite number of constraints. However, only a finite number of variables appear in an infinite number of constraints, and only a finite number of constraints have an infinite number of variables. Duality in this class of programs is studied and used to develop a system of nonlinear equations satisfied by optimal solutions of the primal and dual programs. This nonlinear system has uses in numerical techniques for solving separably-infinite programs.

Zusammenfassung

Bei den in diesem Beitrag untersuchten separabel-infiniten Programmen handelt es sich um lineare Programme mit unendlich vielen Variablen und unendlich vielen Nebenbedingungen, wobei nur endlich viele Variablen in unendlich vielen Nebenbedingungen vorkommen und nur endlich viele Nebenbedingungen unendlich viele Variablen haben. Für diese Programme, die in einem engen Zusammenhang zu semi-infiniten Programmen stehen, wird eine Dualitätstheorie entwickelt, die Grundlage für numerische Verfahren zur Lösung von separabel-infiniten Programmen ist.

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Authors and Affiliations

  1. Center for Cybernetic Studies, The University of Texas at Austin, 78712, Austin, Texas, USA

    A. Charnes (Director)

  2. Department of Mathematics, Carnegie-Mellon University, 15213, Pittsburgh, Pennsylvania, USA

    P. R. Gribik & K. O. Kortanek

Authors
  1. A. Charnes
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  2. P. R. Gribik
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  3. K. O. Kortanek
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Additional information

Research partially supported by the Office of Naval Research, Contract No. N00014-75-C-0569.

Research partially supported by National Science Foundation, Grant NSF ENG76-05191.

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Charnes, A., Gribik, P.R. & Kortanek, K.O. Separably-infinite programs. Zeitschrift für Operations Research 24, 33–45 (1980). https://doi.org/10.1007/BF01920270

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  • DOI: https://doi.org/10.1007/BF01920270

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