# An exterior-point method for linear programming problems

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## Abstract

This paper proves the convergence of an algorithm for solving linear programming problems in*O(mn*^{2}) arithmetic operations. The method is called an exterior-point procedure, because it obtains a sequence of approximations falling outside the set*U* of feasible solutions. Each iteration consists of a single step within some constraining hyperplane, followed by one or more projections which force the new approximation to fall within some envelope about*U*. The paper also discusses several numerical applications. In some types of problems, the method is considerably faster than a standard simplex method program when the size of the problem is sufficiently large.

### Key Words

Linear programming polynomial time algorithms## Preview

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### References

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## Copyright information

© Plenum Publishing Corporation 1996