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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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


Author: Dinh The Luc
Journal: Proc. Amer. Math. Soc. 125 (1997), 555-567
MSC (1991): Primary 52A20, 90C31
MathSciNet review: 1343711
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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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Additional Information

Dinh The Luc
Affiliation: Université d’Avignon, 33 rue Louis Pasteur, Avignon, France
Address at time of publication: Institute of Mathematics, P. O. Box 631, Hanoi, Vietnam

DOI: http://dx.doi.org/10.1090/S0002-9939-97-03507-7
PII: S 0002-9939(97)03507-7
Keywords: Polyhedral convex set, representing point and direction, sensitivity analysis, parametric linear problem, parametric concave problem, parametric polyhedral problem
Received by editor(s): January 25, 1995
Received by editor(s) in revised form: May 17, 1995
Additional Notes: The author is on leave from the Institute of Mathematics, Hanoi, Vietnam
Communicated by: Joseph S. B. Mitchell
Article copyright: © Copyright 1997 American Mathematical Society