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Lagrangian Subgradients

Author

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  • Richard C. Grinold

    (University of California, Berkeley)

Abstract

There is a dual program linked with every nonlinear program. The dual objective function is called the Lagrangian; it is defined in terms of the original problem. This note presents a characterization of the Lagrangian subgradients under general conditions. The theorem follows from a result of Danskin [1] that can be used (see [2]) to characterize the Lagrangian directional derivatives. These characterizations are theoretically interesting and may be useful in computing optimal dual solutions. Rockafellar's outstanding book, [3], is used as a basic reference; it contains a wealth of background and historical information.

Suggested Citation

  • Richard C. Grinold, 1970. "Lagrangian Subgradients," Management Science, INFORMS, vol. 17(3), pages 185-188, November.
    • Handle: RePEc:inm:ormnsc:v:17:y:1970:i:3:p:185-188
    DOI: 10.1287/mnsc.17.3.185
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    Cited by:

    1. Claude Lemaréchal, 2007. "The omnipresence of Lagrange," Annals of Operations Research, Springer, vol. 153(1), pages 9-27, September.
    2. Olivier Morand & Kevin Reffett & Suchismita Tarafdar, 2018. "Generalized Envelope Theorems: Applications to Dynamic Programming," Journal of Optimization Theory and Applications, Springer, vol. 176(3), pages 650-687, March.

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