Lipschitz and differentiability properties of quasi-concave and singular normal distribution functions

René Henrion; Werner Römisch

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SPEPS Preprint

Author(s):	René Henrion, Weierstrass Institute Werner Römisch, Humboldt-University Berlin
Title:	Lipschitz and differentiability properties of quasi-concave and singular normal distribution functions
Date of Acceptance:	26.04.2005
Submission Date:	07.01.2005
Series Title:	Stochastic Programming E-Print Series (SPEPS)
Editors:	Julie L. Higle; Werner Römisch; Surrajeet Sen
Complete Preprint:	pdf (urn:nbn:de:kobv:11-10059851)
Keywords (eng):	differentiability, probabilistic constraints, stochastic optimization, quasi-concave measures, singular normal distributions, Lipschitz continuity
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Abstract (eng):

The paper provides a condition for differentiability as well as an equivalent criterion for Lipschitz continuity of singular normal distributions. Such distributions are of interest, for instance, in stochastic optimization problems with probabilistic constraints, where a comparatively small (nondegenerate-) normally distributed random vector induces a large number of linear inequality constraints (e.g. networks with stochastic demands). The criterion for Lipschitz continuity is established for the class of quasi-concave distributions which the singular normal distribution belongs to.

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