Stability of the optimal basis of a linear program under uncertainty

Authors:
Jiri Rohn
Affiliations:
Faculty of Mathematics and Physics, Charles University, Malostranske nam. 25, 11800 Prague, Czechoslovakia
Venue:
Operations Research Letters
Year:
1993

Citing 0
Cited 1

Accurate solution of dense linear systems, Part II: Algorithms using directed rounding

Journal of Computational and Applied Mathematics

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Abstract

We prove that the set of optimal basic variables of a linear program remains stable under mutually independent variations of all data within prescribed tolerances if and only if it is stable for a finite subset of explicitly described linear programs from this family. The cardinality of this subset is exponential in the number of constraints.