On the uniqueness of the optimal solution in linear programming

Authors

  • Peter Szilágyi Szent Istvan University, Budapest, Hungary

Keywords:

linear programming, optimality conditions, constraint qualifications, complementarity, duality, theorems of the alternative

Abstract

In this paper numerous necessary and sufficient conditions will be given for a vector to be the unique optimal solution of the primal problem, as well as for that of the dual problem, and even for the case when the primal and the dual problem have unique optimal solutions at the same time, respectively, by means of using the strict complementarity and the linear independence constraint qualification. Beyond that, the topological structure of the optimal solutions satisfying the strict complementarity will be determined.

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References

Kyparisis, J. On uniqueness of Kuhn-Tucker multipliers in nonlinear programming, Mathematical Programming, 32, pp. 242-246, 1985, https://doi.org/10.1007/bf01586095

Mangasarian, O. L. Nonlinear programming, McGraw-Hill, New York, 1969.

Mangasarian, O. L. Uniqueness of solution in linear programming, Linear Algebra and its Applications, 25, pp. 151-162, 1979, https://doi.org/10.1016/0024-3795(79)90014-4

Szilágyi, P. Nonhomogeneous linear theorems of the alternative, Pure Mathematics and Applications, 10, pp. 141-159, 1999.

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Published

2006-08-01

How to Cite

Szilágyi, P. (2006). On the uniqueness of the optimal solution in linear programming. Rev. Anal. Numér. Théor. Approx., 35(2), 225–244. Retrieved from https://ictp.acad.ro/jnaat/journal/article/view/2006-vol35-no2-art11

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Articles