TY - JOUR

T1 - FAMILY OF SIMPLEX VARIANTS SOLVING AN M multiplied by D LINEAR PROGRAM IN EXPECTED NUMBER OF PIVOT STEPS DEPENDING ON D ONLY.

AU - Adler, Ilan

AU - Karp, Richard

AU - Shamir, Ron

PY - 1986

Y1 - 1986

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0022806252&partnerID=8YFLogxK

U2 - 10.1287/moor.11.4.570

DO - 10.1287/moor.11.4.570

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AN - SCOPUS:0022806252

VL - 11

SP - 570

EP - 590

JO - Mathematics of Operations Research

JF - Mathematics of Operations Research

SN - 0364-765X

IS - 4

ER -