Abstract
This paper builds upon the relationship between the objective function of a semi-infinite linear program and its constraints to identify a class of semi-infinite linear programs which do not have a duality gap. The key idea is to guarantee the approximation of the primal program by a sequence of linear programs where thenth approximating program is to minimize the objective function subject to the firstn constraints. The paper goes on to show that any program not in the identified class can be linearly perturbed into it with the optimal value of the perturbed program converging to the optimal value of the original program. The results are then extended to the case when an uncountable number of constraints are present by reducing this case to the countable case.
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Some of the results of this paper are in partial fulfillment of the requirements for the degree of Doctor of Philosophy.
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Karney, D.F. Duality gaps in semi-infinite linear programming—an approximation problem. Mathematical Programming 20, 129–143 (1981). https://doi.org/10.1007/BF01589340
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DOI: https://doi.org/10.1007/BF01589340