# A Simple Projection Algorithm for Linear Programming Problems

Tomonari Kitahara, Noriyoshi Sukegawa

1 引用 (Scopus)

### 抄録

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.

元の言語 英語 167-178 12 Algorithmica 81 1 https://doi.org/10.1007/s00453-018-0436-3 出版済み - 1 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

### これを引用

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

：: Algorithmica, 巻 81, 番号 1, 15.01.2019, p. 167-178.

Kitahara, Tomonari ; Sukegawa, Noriyoshi. / A Simple Projection Algorithm for Linear Programming Problems. ：: Algorithmica. 2019 ; 巻 81, 番号 1. pp. 167-178.
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