Nonlinear OneParametric Bottleneck Linear Programming
Schubert, I. S. and Zimmermann, Uwe
(1985)
Nonlinear OneParametric Bottleneck Linear Programming.
Published in:
Zeitschrift für OperationsResearch : ZOR ; mathematical methods of operations research Vol. 29 (5).
pp. 187201.
Abstract
We consider the oneparametric 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 

Citations:  0 (Google Scholar)  
Uncontrolled Keywords:  linear constraints oneparametric linear bottleneck problem 
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Divisions:  Mathematical Institute 
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ZAIK Number:  zpr84008 

Depositing User:  Archive Admin 
Date Deposited:  02 Apr 2001 00:00 
Last Modified:  19 Jan 2012 12:45 
URI:  http://earchive.informatik.unikoeln.de/id/eprint/8 