Abstract
We propose a potential-reduction algorithm which always uses the primal—dual affine-scaling direction as a search direction. We choose a step size at each iteration of the algorithm such that the potential function does not increase, so that we can take a longer step size than the minimizing point of the potential function. We show that the algorithm is polynomial-time bounded. We also propose a low-complexity algorithm, in which the centering direction is used whenever an iterate is far from the path of centers.
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This paper is dedicated to Phil Wolfe on the occasion of his 65th birthday.
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Mizuno, S., Nagasawa, A. A primal—dual affine-scaling potential-reduction algorithm for linear programming. Mathematical Programming 62, 119–131 (1993). https://doi.org/10.1007/BF01585163
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DOI: https://doi.org/10.1007/BF01585163