A primal projective interior point method for linear programming |
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Authors: | Donald Goldfarb Dong Xiao |
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Institution: | (1) Department of Industrial Engineering and Operations Research, Columbia University, 10027 New York, NY, USA |
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Abstract: | We present a new projective interior point method for linear programming with unknown optimal value. This algorithm requires only that an interior feasible point be provided. It generates a strictly decreasing sequence of objective values and within polynomial time, either determines an optimal solution, or proves that the problem is unbounded. We also analyze the asymptotic convergence rate of our method and discuss its relationship to other polynomial time projective interior point methods and the affine scaling method.This research was supported in part by NSF Grants DMS-85-12277 and CDR-84-21402 and ONR Contract N00014-87-K0214. |
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Keywords: | Interior point methods linear programming fractional linear programming projective algorithm Karmarkar's algorithm polynomial-type algorithm |
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