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Some Properties of Multiple Parameters Linear Programming
Journal of Inequalities and Applications volume 2010, Article number: 204263 (2010)
We consider a linear programming problem in which the right-hand side vector depends on multiple parameters. We study the characters of the optimal value function and the critical regions based on the concept of the optimal partition. We show that the domain of the optimal value function can be decomposed into finitely many subsets with disjoint relative interiors, which is different from the result based on the concept of the optimal basis. And any directional derivative of at any point can be computed by solving a linear programming problem when only an optimal solution is available at the point.
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Li, M., Li, S. & Yan, H. Some Properties of Multiple Parameters Linear Programming. J Inequal Appl 2010, 204263 (2010). https://doi.org/10.1155/2010/204263
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