Mathematical Programming

, Volume 49, Issue 1–3, pp 7–21

# Polynomial affine algorithms for linear programming

• Clovis C. Gonzaga
Article

## Abstract

The method of steepest descent with scaling (affine scaling) applied to the potential functionq logc′x — ∑i=1n logxi solves the linear programming problem in polynomial time forq ⩾ n. Ifq = n, then the algorithm terminates in no more than O(n2L) iterations; if q ⩾ n +$$\sqrt n$$ withq = O(n) then it takes no more than O(nL) iterations. A modified algorithm using rank-1 updates for matrix inversions achieves respectively O(n4L) and O(n3.5L) arithmetic computions.

### Key words

Linear programming affine algorithms Karmarkar's algorithm interior methods

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