Documentation

linopt::Transparent::dual_prices

Get the dual solution belonging to the given tableau

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Syntax

linopt::Transparent::dual_prices(tableau)

Description

linopt::Transparent::dual_prices(tableau) returns the dual solution of the linear optimization problem given by tableau.

This procedure returns the dual solution belonging to the given tableau in form of a set of lists containing two elements, the first one is a restriction and the second one is the value belonging to the slack variable connected to the restriction in the dual solution.

Examples

Example 1

Here it is demonstrated that the dual solution of the final tableau is similar to the second element of the result of linopt::minimize using the option DualPrices:

First we compute the final tableau of the simplex algorithm:

k := [{x <= 2, y <= 2, x + 2*y >= 4}, - x + y, NonNegative]:
t := linopt::Transparent(k):
t := linopt::Transparent::simplex(t) Now we compute the solutions:

linopt::Transparent::dual_prices(t);
linopt::minimize(k, DualPrices)  delete k, t:

Example 2

We compute the dual solution of another linear program:

k := [{x <= 2, y <= 2, x + 2*y >= 4}, -x + y, NonNegative]:
t := linopt::Transparent(k);
linopt::Transparent::dual_prices(t)  delete k, t:

Parameters

 tableau A simplex tableau of domain type linopt::Transparent

Return Values

Set of lists, each containing 2 elements.

References

Papadimitriou, Christos H; Steiglitz, Kenneth: Combinatorial Optimization; Algorithms and Complexity. Prentice-Hall, 1982.

Nemhauser, George L; Wolsey, Laurence A: Integer and Combinatorial Optimization. New York, Wiley, 1988.

Salkin, Harvey M; Mathur, Kamlesh: Foundations of Integer Programming. North-Holland, 1989.

Neumann, Klaus; Morlock, Martin: Operations-Research. Munich, Hanser, 1993.

Duerr, Walter; Kleibohm, Klaus: Operations Research; Lineare Modelle und ihre Anwendungen. Munich, Hanser, 1992.

Suhl, Uwe H: MOPS - Mathematical OPtimization System. European Journal of Operational Research 72(1994)312-322. North-Holland, 1994.

Suhl, Uwe H; Szymanski, Ralf: Supernode Processing of Mixed Integer Models. Boston, Kluwer Academic Publishers, 1994.