Abstract
For the case of a consistent semi-infinite linear program, we provide several hypotheses, which are both necessary as well as sufficient, that there be no duality gap between the program and its formal dual (with attainment of value in the dual), for every linear objective function. Earlier work provided sufficient conditions for no duality gap for all linear objective functions, or a necessary and sufficient condition for no duality gap for a fixed linear criterion.
The first author’s research has been partially supported by grant DAAG-29-80-C-0637 of the Army Research Office, Research Triangle Park, North Carolina.
The second author’s research has been partially supported by NSF grant ECS8001763.
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Duffin, R.J., Jeroslow, R.G., Karlovitz, L.A. (1983). Duality in Semi-Infinite Linear Programming. In: Fiacco, A.V., Kortanek, K.O. (eds) Semi-Infinite Programming and Applications. Lecture Notes in Economics and Mathematical Systems, vol 215. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-46477-5_4
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DOI: https://doi.org/10.1007/978-3-642-46477-5_4
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