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Directional differentiability of the optimal value function in convex semi-infinite programming

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Abstract

In this paper, directional differentiability properties of the optimal value function of a parameterized semi-infinite programming problem are studied. It is shown that if the unperturbed semi-infinite programming problem is convex, then the corresponding optimal value function is directionally differentiable under mild regularity assumptions. A max-min formula for the directional derivatives, well-known in the finite convex case, is given.

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Authors and Affiliations

  1. School of Industrial and Systems Engineering, Georgia Institute of Technology, 30332-0205, Atlanta, GA, USA

    Alexander Shapiro

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  1. Alexander Shapiro
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Shapiro, A. Directional differentiability of the optimal value function in convex semi-infinite programming. Mathematical Programming 70, 149–157 (1995). https://doi.org/10.1007/BF01585933

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  • DOI: https://doi.org/10.1007/BF01585933

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