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2003-02-10Buch DOI: 10.18452/8285
Perturbation ananlysis of chance-constrained programs under variation of all constraint data
dc.contributor.authorHenrion, René
dc.contributor.editorHigle, Julie L.
dc.contributor.editorRömisch, Werner
dc.contributor.editorSen, Surrajeet
dc.date.accessioned2017-06-16T19:51:08Z
dc.date.available2017-06-16T19:51:08Z
dc.date.created2006-02-22
dc.date.issued2003-02-10
dc.date.submitted2003-01-09
dc.identifier.urihttp://edoc.hu-berlin.de/18452/8937
dc.description.abstractA fairly general shape of chance constraint programs is\[(P) min \{ g(x) | x \in X, \mu (H(x)) \le p \} ,\]where $g : \R^m \to \R$ is a continuous objective function, $X \subseteq \R^m$ is a closed subset of deterministic constraints, and the inequality defines a probabilistic constraint with $H : \R^m \to \atop \to \R^s$ being a multifunction with closed graph, $\mu$ is a probability measure on $\rR^s$ and $p \in (0,1)$ is some probability level. In the simplest case of linear chance constraints, $g$ is linear, $X$ is a polyhedron and $H(x) = \{ z \in \R^s | Ax \ge z\} $, where $A$ is a matrix of order $(s,m)$ and the inequality sign has to be understood component-wise.\\Since the data of optimization problems are typically uncertain or approximated by other data which are easier to handle, the question of stability of solutions arises naturally. Concerning $(P)$, the first idea is to investigate solutions under perturbations of the right hand side $p$ of the inequality. This reflects the modeling degree of freedom when choosing a probability at which the constraint system is supposed to be valid. Furthermore, the probability measure $\mu$ is unknown in general and has to be approximated, for instance, by empirical measures. This motivates to extend the perturbation analysis to $\mu$. Stability of solutions of $(P)$ with respect to $p$ and $\mu$ is well understood now but shall be briefly reviewed in this paper for the sake of being selfcontained. Apart from these two constraint parameters, also approximations of the deterministic constraint $X$ and of the random set mapping $H$ in $(P)$ may be of interest. The aim of this paper is to identify constraint qualifications for stability under partial p erturbations of the single constraint parameters in $(P)$. Due to the increasing complexity of how these parameters influence each other, the resulting constraint qualifications become more and more restrictive when passing from $p$ over $\mu$ to $X$ and $H$. Part of the result relate to convex data in $(P)$ or even in the perturbations of $(P)$. Special emphasis is put on a series of counter-examples highlighting the necessity and limitations of the obtained conditions.eng
dc.language.isoeng
dc.publisherHumboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, Institut für Mathematik
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/
dc.subject.ddc510 Mathematik
dc.titlePerturbation ananlysis of chance-constrained programs under variation of all constraint data
dc.typebook
dc.identifier.urnurn:nbn:de:kobv:11-110-18452/8937-7
dc.identifier.doihttp://dx.doi.org/10.18452/8285
local.edoc.container-titleStochastic Programming E-Print Series
local.edoc.type-nameBuch
local.edoc.container-typeseries
local.edoc.container-type-nameSchriftenreihe
local.edoc.container-publisher-nameSpringer
local.edoc.container-publisher-placeBerlin
local.edoc.container-volume2003
local.edoc.container-issue3
local.edoc.container-year2004
local.edoc.container-erstkatid2936317-2

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