The method of steepest descent with scaling (affine scaling) applied to the potential functionq logc′x — ∑ i=1 n logx i solves the linear programming problem in polynomial time forq ? n. Ifq = n, then the algorithm...
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The method of steepest descent with scaling (affine scaling) applied to the potential functionq logc′x — ∑ i=1 n logx i solves the linear programming problem in polynomial time forq ? n. Ifq = n, then the algorithm terminates in no more than O(n 2 L) 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(n 4 L) and O(n 3.5 L) arithmetic computions.
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