The dual of the dual as an approximation of the primal

A formulation and some properties of the (Lagrangian) dual of the dual of a mathematical programming problem were presented in an article by Unger and Hurter (1972). Here, that formulation is simplified, so that the resulting form is more closely related to the primal. In particular, the dual of the...

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Bibliographic Details
Published in:International journal of systems science 1974-12, Vol.5 (12), p.1119-1130
Main Authors: UNGER, P.S., HURTER, A.P.
Format: Article
Language:English
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Summary:A formulation and some properties of the (Lagrangian) dual of the dual of a mathematical programming problem were presented in an article by Unger and Hurter (1972). Here, that formulation is simplified, so that the resulting form is more closely related to the primal. In particular, the dual of the dual is shown to be merely the primal, except that the objective function and each constraint are replaced by their first-order Taylor series approximation. This formulation is used to obtain new bounds for the primal, and necessary conditions for the convexity of the dual problem, and for the absence of a duality gap. The relationship of the dual of the dual to condensation in geometric programming is described. The dual of the dual is related to several existing mathematical programming algorithms.
ISSN:0020-7721
1464-5319
DOI:10.1080/00207727408920166