Linear-fractional programming: Difference between revisions

Revision as of 17:20, 16 April 2023

Revision as of 17:22, 16 April 2023

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& t \geq 0.

\end{align}

</math>

</math>A solution <math>\mathbf{x}</math> to the original linear-fractional program can be translated to a solution of the transformed program via the equalities

</math>A solution <math>\mathbf{x}</math> to the original linear-fractional program can be translated to a solution of the transformed linear program via the equalities

:<math>\mathbf{y} = \frac{1}{\mathbf{d}^T \mathbf{x} + \beta} \cdot \mathbf{x}\quad \text{and} \quad t = \frac{1}{\mathbf{d}^T \mathbf{x} + \beta}.</math>

Conversely, a solution for <math>\mathbf{y}</math> and <math>t </math> of the transformed linear program can be translated to a solution of the original problemlinear-fractional program via

:<math>\mathbf{x}=\frac{1}{t}\mathbf{y}.</math>