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Ordinary convex programs without a duality gap

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Abstract

In the Kuhn-Tucker theory of nonlinear programming, there is a close relationship between the optimal solutions to a given minimization problem and the saddlepoints of the corresponding Lagrangian function. It is shown here that, if the constraint functions and objective function arefaithfully convex in a certain broad sense and the problem has feasible solutions, then theinf sup andsup inf of the Lagrangian are necessarily equal.

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References

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Authors and Affiliations

  1. University of Washington, Seattle, Washington

    R. T. Rockafellar (Professor of Mathematics)

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  1. R. T. Rockafellar
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Communicated by M. R. Hestenes

This work was supported in part by the Air Force Office of Scientific Research under Grant No. AF-AFOSR-1202-67B.

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Rockafellar, R.T. Ordinary convex programs without a duality gap. J Optim Theory Appl 7, 143–148 (1971). https://doi.org/10.1007/BF00932472

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  • DOI: https://doi.org/10.1007/BF00932472

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