A FEASIBILITY CONJECTURE RELATED TO THE HIRSCH CONJECTURE,

Abstract

A very important unsolved problem in linear programming today is the validity or nonvalidity of the conjecture which follows: Hirsch Conjecture: let X and Y be feasible bases to the linear programming problem Y > or = O, X > or = O, IY + BX = b and let m be the rank of this system. Then the conjecture is that there exists a sequence of m feasible pivot operations that transforms the system into Y > or = O , X > or = O, (1/B)Y + IX = (1/B)b. That is to say a sequence such that each of the m - l intermediate bases is feasible.

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Document Details

Document Type
Technical Report
Publication Date
Oct 23, 1964
Accession Number
AD0610951

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  • Richard Wollmer

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  • University of California, Berkeley

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