Abstract
For the problemP(λ): Maximizec T z subject toz∈Z(λ), whereZ(λ) is defined by an in general infinite set of linear inequalities, it is shown that the value-function has directional derivatives at every point\(\bar \lambda \) such thatP(\(\bar \lambda \)) and its dual are both superconsistent. To compute these directional derivatives a min-max-formula, well-known in convex programming, is derived. In addition, it is shown that derivatives can be obtained more easily by a limit-process using only convergent selections of solutions ofP(λ n ), λ n →\(\bar \lambda \) and their duals.
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Zencke, P., Hettich, R. Directional derivatives for the value-function in semi-infinite programming. Mathematical Programming 38, 323–340 (1987). https://doi.org/10.1007/BF02592018
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DOI: https://doi.org/10.1007/BF02592018