Abstract
In this paper, we provide a systematic approach to the main topics in linear semi-infinite programming by means of a new methodology based on the many properties of the sub-differential mapping and the closure of a given convex function. In particular, we deal with the duality gap problem and its relation to the discrete approximation of the semi-infinite program. Moreover, we have made precise the conditions that allow us to eliminate the duality gap by introducing a perturbation in the primal objective function. As a by-product, we supply different extensions of well-known results concerning the subdifferential mapping.
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Communicated by R. A. Tapia
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Goberna, M.A., Lopez, M.A. Optimal value function in semi-infinite programming. J Optim Theory Appl 59, 261–279 (1988). https://doi.org/10.1007/BF00938312
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DOI: https://doi.org/10.1007/BF00938312