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# `linopt`::`Transparent::autostep`

Perform the next simplex step

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## Syntax

```linopt::Transparent::autostep(`tableau`)
```

## Description

`linopt::Transparent::autostep(tableau)` performs the next step of the simplex algorithm. This is the same step that `linopt::Transparent::suggest` would suggest for the given simplex tableau `tableau`.

Normally `linopt::Transparent::autostep` returns the next simplex tableau. If the calculation of the simplex algorithm is finished `linopt::Transparent::autostep` returns a set containing a solution of the given linear program described by `tableau`.

## Examples

### Example 1

The ordinary simplex tableau of a given linear program is created:

```k := [{x + y >= 2}, x, NonNegative]: t := linopt::Transparent(k)```

The next two steps of the simplex algorithm are executed for the given simplex tableau:

```linopt::Transparent::autostep(t); linopt::Transparent::autostep(%)```

`delete k, t:`

### Example 2

The ordinary simplex tableau of a given linear program is created:

```k := [{x + y >= -1, x + y <= 3}, x + 2*y, NonNegative]: t := linopt::Transparent(k)```

If the end of the simplex algorithm is reached, `linopt::Transparent::autostep` returns a solution of the given linear program:

```linopt::Transparent::suggest(t), linopt::Transparent::autostep(t)```

`delete k, t:`

## Parameters

 `tableau` A simplex tableau of domain type `linopt::Transparent`

## Return Values

Simplex tableau of domain type `linopt::Transparent` or a set which contains the solution of the linear program.

## 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.

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