Linear-fractional programming: Difference between revisions

Revision as of 17:41, 27 September 2013

Revision as of 12:36, 30 October 2013

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==Transformation to a linear program==

Under the assumption that the feasible region is non-empty and bounded, the Charnes-Cooper transformation <math>\mathbf{y} = \frac{1}{\mathbf{d}^T \mathbf{x} + \beta} \cdot \mathbf{x}; t = \frac{1}{\mathbf{d}^T \mathbf{x} + \beta}</math><ref name="CC"/> translates the linear-fractional program above to the equivalent linear program

Under the assumption that the feasible region is non-empty and bounded, the Charnes-Cooper transformation<ref name="CC"/>

:<math>

<math>\mathbf{y} = \frac{1}{\mathbf{d}^T \mathbf{x} + \beta} \cdot \mathbf{x}\;;\;\; t = \frac{1}{\mathbf{d}^T \mathbf{x} + \beta}</math>

translates the linear-fractional program above to the equivalent linear program:

:<math>

\begin{align}

\text{maximize} \quad & \mathbf{c}^T \mathbf{y} + \alpha t \\