Ideas Leading to a Better Bound on the Average Number of Pivot Steps for Solving an LP

Abstract

This paper deals with the complexity of the solution-process of linear programming problems of the following type:

$$ {\begin{array}{*{20}c} {{\text{maximize }}v^T x} \\ {{\text{subject to a}}_1^T x \leqslant 1,...,{\text{a}}_m^T x \leqslant 1(1)} \\ {{\text{where }}x,v,a_1 ,...,a_m \in {\text{IR}}^n {\text{and }}m \geqslant n.} \\ \end{array} } $$

(1)

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