, Volume 40, Issue 1-3, pp 59-93

A polynomial-time algorithm, based on Newton's method, for linear programming

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A new interior method for linear programming is presented and a polynomial time bound for it is proven. The proof is substantially different from those given for the ellipsoid algorithm and for Karmarkar's algorithm. Also, the algorithm is conceptually simpler than either of those algorithms.

This research was supported by an NSF Mathematical Sciences Postdoctoral Research Fellowship and by NSF Grant 8120790. The research was performed at the Mathematical Sciences Research Institute in Berkeley, California.