A Simple Projection Algorithm for Linear Programming Problems

Tomonari Kitahara, Noriyoshi Sukegawa

Research output: Contribution to journalArticle

2 Citations (Scopus)

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 languageEnglish
Pages (from-to)167-178
Number of pages12
JournalAlgorithmica
Volume81
Issue number1
DOIs
Publication statusPublished - Jan 15 2019

All Science Journal Classification (ASJC) codes

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

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