Lagrangian Subgradients

Richard C. Grinold
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Richard C. Grinold: University of California, Berkeley

Management Science, 1970, vol. 17, issue 3, 185-188

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.

Date: 1970
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