Polynomial affine algorithms for linear programming |
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Authors: | Clovis C. Gonzaga |
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Affiliation: | (1) Department of Systems Engineering and Computer Sciences, COPPE-Federal University of Rio de Janeiro, 21941 Rio de Janeiro, RJ, Brasil |
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Abstract: | The method of steepest descent with scaling (affine scaling) applied to the potential functionq logcx — 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 + 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. |
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Keywords: | Linear programming affine algorithms Karmarkar's algorithm interior methods |
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