### Abstract

Fujishige et al. propose the LP-Newton method, a new algorithm for linear programming problem (LP). They address LPs which have a lower and an upper bound for each variable, and reformulate the problem by introducing a related zonotope. The LP-Newton method repeats projections onto the zonotope by Wolfe’s algorithm. For the LP-Newton method, Fujishige et al. show that the algorithm terminates in a finite number of iterations. Furthermore, they show that if all the inputs are rational numbers, then the number of projections is bounded by a polynomial in L, where L is the input length of the problem. In this paper, we propose a modification to their algorithm using a binary search. In addition to its finiteness, if all the inputs are rational numbers and the optimal value is an integer, then the number of projections is bounded by L+ 1 , that is, a linear bound.

Original language | English |
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Pages (from-to) | 167-178 |

Number of pages | 12 |

Journal | Algorithmica |

Volume | 81 |

Issue number | 1 |

DOIs | |

Publication status | Published - Jan 15 2019 |

### All Science Journal Classification (ASJC) codes

- Computer Science(all)
- Computer Science Applications
- Applied Mathematics

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## Cite this

*Algorithmica*,

*81*(1), 167-178. https://doi.org/10.1007/s00453-018-0436-3