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dc.contributor.authorVavasis, Stephen A.en_US
dc.contributor.authorYe, Yinyuen_US
dc.description.abstractWe propose a "layered-step" interior point (LIP) algorithm for linear programming. This algorithm follows the central path, either with short steps or with a new type of step called a "layered least squares" (LLS) step. The algorithm returns the exact global minimum after a finite number of steps-in particular, after $O(n^{3.5}c(A))$ iterations, where $c(A)$ is a function of the coefficient matrix. The LLS steps can be thought of as accelerating a path-following interior point method whenever near-degeneracies occur. One consequence of the new method is a new characterization of the central path: we show that it composed of at most $n^2$ alternating straight and curved segments. If the LIP algorithm is applied to integer data, we get as another corollary a new proof of a well-known theorem by Tardos that linear programming can be solved in strongly polynomial time provided that $A$ contains small-integer entries.en_US
dc.format.extent4576539 bytes
dc.format.extent865230 bytes
dc.publisherCornell Universityen_US
dc.subjectcomputer scienceen_US
dc.subjecttechnical reporten_US
dc.titleAn Accelerated Interior Point Method Whose Running Time Depends Only on $A$en_US
dc.typetechnical reporten_US

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