| 11. | Description : For long, there was no provably polynomial time algorithm for the linear programming problem.
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| 12. | The original applications were to give polynomial-time algorithms for integer linear programming problem in fixed dimensions.
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| 13. | During an iteration, an approximating linear programming problem is solved to obtain a candidate for the optimal solution.
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| 14. | This information is used to improve the approximating linear programming problem used for the next iteration of the algorithm.
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| 15. | Essentially, these methods attempt to find the shortest pivot path on the arrangement polytope under the linear programming problem.
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| 16. | If the objective function and all of the hard constraints are linear, then the problem is a linear programming problem.
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| 17. | The Nash equilibrium for a two-player, zero-sum game can be found by solving a linear programming problem.
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| 18. | For example, in solving the linear programming problem, the active set gives the hyperplanes that intersect at the solution point.
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| 19. | :: But don't linear programming problems have Ax \ le b, whereas my problem has Ax < b.
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| 20. | :A feasible solution to a linear programming problem ( or any other Gandalf61 15 : 36, 18 January 2006 ( UTC)
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