Nonlinear One-Parametric Bottleneck Linear Programming
Schubert, I. S. and Zimmermann, Uwe
(1985)
Nonlinear One-Parametric Bottleneck Linear Programming.
Published in:
Zeitschrift für Operations-Research : ZOR ; mathematical methods of operations research Vol. 29 (5).
pp. 187-201.
Abstract
We consider the one-parametric linear bottleneck problem min{c(x,t)| x in P(t)} where the bottleneck objective c(x,t):= max{cj(t) | xj>0} is minimized subject to linear constraints, i.e. P(t):={x| A(t)x=b(t), x>=0}. All coefficients are assumed to be continuous functions of one real parameter t which varies in a real interval S. A method is developed for constructing a partition of S into subintervals on which either a basis stays optimal or the problem stays infeasible. Finiteness of the partition is due to certain finiteness assumptions on the zeros of particular combinations of the coefficient functions. Using a lexicographic refinement of the objective function a characterization of the optimality interval of a fixed basis is derived which is independent on explicit information about other bases.
Item Type: | Article |
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Citations: | 0 (Google Scholar) | |
Uncontrolled Keywords: | linear constraints one-parametric linear bottleneck problem |
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Divisions: | Mathematical Institute |
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ZAIK Number: | zpr84-008 |
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Depositing User: | Archive Admin |
Date Deposited: | 02 Apr 2001 00:00 |
Last Modified: | 19 Jan 2012 12:45 |
URI: | http://e-archive.informatik.uni-koeln.de/id/eprint/8 |