Polynomial affine algorithms for linear programming
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 wordsLinear programming affine algorithms Karmarkar's algorithm interior methods
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