A Simple Projection Algorithm for Linear Programming Problems

Tomonari Kitahara, Noriyoshi Sukegawa

Research output: Contribution to journalArticle

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.

LanguageEnglish
Pages167-178
Number of pages12
JournalAlgorithmica
Volume81
Issue number1
DOIs
Publication statusPublished - Jan 15 2019

Fingerprint

Projection Algorithm
Linear programming
Newton-Raphson method
Zonotope
Newton Methods
Projection
Binary search
Polynomials
Terminate
Finiteness
Upper bound
Iteration
Polynomial
Integer

All Science Journal Classification (ASJC) codes

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

Cite this

A Simple Projection Algorithm for Linear Programming Problems. / Kitahara, Tomonari; Sukegawa, Noriyoshi.

In: Algorithmica, Vol. 81, No. 1, 15.01.2019, p. 167-178.

Research output: Contribution to journalArticle

Kitahara, Tomonari ; Sukegawa, Noriyoshi. / A Simple Projection Algorithm for Linear Programming Problems. In: Algorithmica. 2019 ; Vol. 81, No. 1. pp. 167-178.
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