Abstract
In a linear programming problem with a vector parameter appearing on the right-hand side, the minimum value of the objective is a polyhedral function of this parameter. We show how different characterizations of a polyhedral function correspond to different ways of solving the right-hand side multiparameteric linear programming problem.
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References
T. Gal, andNedoma, J.,Multiparametric Linear Programming, Management Science, Vol. 18, pp. 406–422, 1972.
Gal, T.,Postoptimal Analyses, Parametric Programming, and Related Topics, McGraw Hill, New York, New York, 1979.
Hailperin, T.,Best Possible Inequalities for the Probability of a Logical Function of Events, American Mathematical Monthly, Vol. 72, pp. 343–359, 1965.
Stoer, J., andWitzgall, C.,Convexity and Optimization in Finite Dimensions, I, Springer-Verlag, New York, New York, 1970.
Rockafellar, R. T.,Convex Analysis, Princeton University Press, Princeton, New Jersey, 1969.
Murty, K.,Linear and Combinatorial Programming, John Wiley and Sons, New York, New York, 1976.
Manas, M., andNedoma, J.,Findings All Vertices of a Convex Polyhedron, Numerische Mathematik, Vol. 12, pp. 226–229, 1968.
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Communicated by P. L. Yu
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Schechter, M. Polyhedral functions and multiparametric linear programming. J Optim Theory Appl 53, 269–280 (1987). https://doi.org/10.1007/BF00939219
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DOI: https://doi.org/10.1007/BF00939219