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