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## Linear Program |

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z | overview |

The minimization of a linear function

For the concrete example

min

we have

The figure illustrates a geometric construction of the solution. The solution is the point where a level line of the target function touches the shaded admissible region. Clearly, the target function increases (decreases) if the level lines begin to intersect (not intersect) the admissible region.

If the rows of , which are multiplied with positive , are linearly independent, the characterization is an immediate consequence of the Kuhn-Tucker conditions for the general nonlinear case. For linear problems, redundant constraints, which cause linear dependence, can be omitted, and we can restrict ourselves to the nondegenerate case.

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automatisch erstellt am 26. 1. 2017 |