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On Finding Primal and DualOptimal Bases
 ORSA Journal on Computing
, 1991
"... . We show that if there exists a strongly polynomial time algorithm that finds a basis which is optimal for both the primal and the dual problems, given an optimal solution for one of the problems, then there exists a strongly polynomial algorithm for the general linear programming problem. On other ..."
Abstract

Cited by 49 (1 self)
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. We show that if there exists a strongly polynomial time algorithm that finds a basis which is optimal for both the primal and the dual problems, given an optimal solution for one of the problems, then there exists a strongly polynomial algorithm for the general linear programming problem. On other hand, we give a strongly polynomial time algorithm that finds such a basis, given any pair of optimal solutions (not necessarily basic) for the primal and the dual problems. Such an algorithm is needed when one is using an interior point method and is interested in finding a basis which is both primal and dualoptimal. Subject classification: Programming, Linear, Algorithms and Theory Introduction The reader is referred, for example, to [2] for information about standard results in linear programming which are used in this work. The simplex method for linear programminghas the nice property that if the problem has an optimal solution then a basis is found which is both primaloptimal and ...