Abstract
This paper develops a wholly linear formulation of the posynomial geometric programming problem. It is shown that the primal geometric programming problem is equivalent to a semi-infinite linear program, and the dual problem is equivalent to a generalized linear program. Furthermore, the duality results that are available for the traditionally defined primal-dual pair are readily obtained from the duality theory for semi-infinite linear programs. It is also shown that two efficient algorithms (one primal based and the other dual based) for geometric programming actually operate on the semi-infinite linear program and its dual.
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Communicated by M. Avriel
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Rajgopal, J., Bricker, D.L. Posynomial geometric programming as a special case of semi-infinite linear programming. J Optim Theory Appl 66, 455–475 (1990). https://doi.org/10.1007/BF00940932
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DOI: https://doi.org/10.1007/BF00940932