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 -