FAMILY OF SIMPLEX VARIANTS SOLVING AN M multiplied by D LINEAR PROGRAM IN EXPECTED NUMBER OF PIVOT STEPS DEPENDING ON D ONLY.

Ilan Adler, Richard Karp, Ron Shamir

Research output: Contribution to journalArticlepeer-review

Abstract

The authors present a family of variants of the Simplex method, which are based on a Constraint-By-Constraint procedure: the solution to a linear program is obtained by solving a sequence of subproblems with an increasing number of constraints. We discuss several probabilistic models for generating linear programs. In all of them the underlying distribution is assumed to be invariant under changing the signs of rows or columns in the problem data. A weak regularity condition is also assumed. Under these models, for linear programs with d variables and m multiplied by d inequality constraints, the expected number of pivots required by these algorithms is bounded by a function of min(m,d) only.

Original languageEnglish
Pages (from-to)570-590
Number of pages21
JournalMathematics of Operations Research
Volume11
Issue number4
DOIs
StatePublished - 1986
Externally publishedYes

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