Linear-fractional programming: Difference between revisions

Revision as of 13:33, 30 August 2023

Revision as of 13:35, 30 August 2023

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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{\mathbf{x}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 linear-fractional program via