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A simple proof of a general duality theorem of convex programming

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Zusammenfassung

Im ersten Abschnitt dieses Beitrags demonstrieren wir in kurzer, symbolischlogischer Form die Relationen zwischenUzawas undKuhn undTuckers Äquivalenzsätzen des nichtlinearen Programmierens. Im zweiten Teil geben wir mathematische Beweise zweier Lemmata, die dieKuhn-Tucker-Bedingungen und duale Lösungen in Zusammenhang bringen, und benützen sie und die logische Struktur des ersten Teils, um ein nichtlineares Dualitätstheorem von besonderer Allgemeinheit zu beweisen.

Summary

The first part of this note presents concisely and partially proves in logical terms the relations betweenUzawa's andKuhn andTucker's equivalence theorems of nonlinear programming. In the second part we give simple mathematical proofs of two lemmata linking theKuhn-Tucker conditions and dual solutions and use them to establish a nonlinear duality theorem of considerable generality.

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References

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Authors and Affiliations

  1. University of Alberta, Edmonton, Canada

    B. v. Hohenbalken

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  1. B. v. Hohenbalken
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Additional information

The author is indebted toP. Van Moeseke for teaching him programming theory some time ago, and toD. Bent for helpful comments and criticism.

Vorgel. v.:G. Tintner.

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v. Hohenbalken, B. A simple proof of a general duality theorem of convex programming. Unternehmensforschung Operations Research 13, 29–36 (1969). https://doi.org/10.1007/BF01919548

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  • DOI: https://doi.org/10.1007/BF01919548

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