Smooth representation of a parametric polyhedral convex set with application to sensitivity in optimization

Luc, Dinh

doi:10.1090/S0002-9939-97-03507-7

Smooth representation of a parametric polyhedral convex set with application to sensitivity in optimization
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by Dinh The Luc

Proc. Amer. Math. Soc. 125 (1997), 555-567

DOI: https://doi.org/10.1090/S0002-9939-97-03507-7

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Abstract:

We show in this paper that if a polyhedral convex set is defined by a parametric linear system with smooth entries, then it possesses local smooth representation almost everywhere. This result is then applied to study the differentiability of the solutions and the marginal functions of several classes of parametric optimization problems.

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