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Algorithmica

pp 1–12 | Cite as

A Simple Projection Algorithm for Linear Programming Problems

  • Tomonari Kitahara
  • Noriyoshi Sukegawa
Article
  • 61 Downloads

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.

Keywords

Linear programming Zonotope Projection Binary search 

Notes

Acknowledgements

The first author is supported in part by Grant-in-Aid for Young Scientists (B) 15K15941 from the Japan Society for the Promotion of Sciences. The second author is supported in part by Grant-in-Aid for Young Scientists (Start-up) 15H06617 from the Japan Society for the Promotion of Sciences.

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Economic Engineering, Faculty of EconomicsKyushu UniversityFukuoka-shiJapan
  2. 2.Department of Information and System Engineering, Faculty of Science and EngineeringChuo UniversityBunkyo-kuJapan

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