# A polynomial projection algorithm for linear feasibility problems

Full Length Paper Series A

- First Online:

- Received:
- Accepted:

DOI: 10.1007/s10107-014-0823-8

- Cite this article as:
- Chubanov, S. Math. Program. (2015) 153: 687. doi:10.1007/s10107-014-0823-8

- 4 Citations
- 454 Downloads

## Abstract

We propose a polynomial algorithm for linear feasibility problems. The algorithm represents a linear problem in the form of a system of linear equations and non-negativity constraints. Then it uses a procedure which either finds a solution for the respective homogeneous system or provides the information based on which the algorithm rescales the homogeneous system so that its feasible solutions in the unit cube get closer to the vector of all ones. In a polynomial number of calls to the procedure the algorithm either proves that the original system is infeasible or finds a solution in the relative interior of the feasible set.

### Keywords

Linear programming Systems of linear inequalities Polynomial algorithm### Mathematics Subject Classification

90C05 Linear programming## Copyright information

© Springer-Verlag Berlin Heidelberg and Mathematical Optimization Society 2014