# Polynomial affine algorithms for linear programming

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## Abstract

The method of steepest descent with scaling (affine scaling) applied to the potential function*q* log*c′x* — ∑_{i=1}^{n} log*x*_{i} solves the linear programming problem in polynomial time for*q ⩾ n.* If*q = n*, then the algorithm terminates in no more than O(*n*^{2}*L*) iterations; if q ⩾ n +\(\sqrt n \) with*q* = O(*n*) then it takes no more than O(*nL*) iterations. A modified algorithm using rank-1 updates for matrix inversions achieves respectively O(*n*^{4}*L*) and O(*n*^{3.5}*L*) arithmetic computions.

### Key words

Linear programming affine algorithms Karmarkar's algorithm interior methods## Preview

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### References

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## Copyright information

© The Mathematical Programming Society, Inc. 1990