# Documentation

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# linopt::Transparent::userstep

Perform a user defined simplex step

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## Syntax

linopt::Transparent::userstep(tableau, basvar, nonbasbar)

## Description

linopt::Transparent::userstep(tableau, basvar, nonbasbar) performs a user defined simplex step in the tableau with the pivot element defined by basvar and nonbasvar.

## Examples

### Example 1

We execute the simplex step given by the pivot element (slk[1],x):

k := [{x + y >= 2}, x, NonNegative]:
t:= linopt::Transparent(k);
linopt::Transparent::userstep(t, slk[1], x)

### Example 2

If we specify a wrong pivot element, we will get an error message:

k := [{3*x + 4*y - 3*z <= 23, 5*x - 4*y - 3*z <= 10,
7*x + 4*y + 11*z <= 30}, -x + y + 2*z, NonNegative]:
t:= linopt::Transparent(k);
linopt::Transparent::userstep(t, x, y)

Error: Pivot element not specified or specified incorrectly. [linopt::Transparent::userstep]
delete k, t:

## Parameters

 tableau A simplex tableau of domain type linopt::Transparent basvar A basic variable represented by an identifier that has to leave the basis nonbasvar A non-basic variable represented by an identifier that has to enter the basis

## Return Values

Simplex tableau of domain type linopt::Transparent.

## 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.