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Questions tagged [generalized-linear-fractional]

1 vote
1 answer
124 views

How to avoid division by zero with a binary variable at the denominator in a network assignment problem?

I am currently working with some network assignment problem as a network engineer. My engineering application can be stated as follows: There are $M$ users that needs to be assign to $N$ servers. This ...
Tuong Nguyen Minh's user avatar
3 votes
0 answers
86 views

Looking for an efficient way to solve a fractional problem (affine function over euclidean norm )

While working on optimization issues I encountered the following problem: $$\left\{\begin{array}{ll} {\displaystyle \sup_{z\in\mathbb{R}^{m}}} &\frac{ \langle c,z \rangle + \rho}{ \left\|B z\...
Diego Fonseca's user avatar
1 vote
2 answers
63 views

Solving single-variable fractional equation

Can anyone advise how this nonlinear equation with a single variable $x$ can be solved as a closed form? ${\left(\frac{x}{1-x}\right)}^2.{\left(\frac{x-C}{\left(1-x\right)-N}\right)}^2=H.\frac{2x-C}{2\...
Reza Farahani's user avatar
6 votes
1 answer
261 views

Is it possible to express these constraints with basic cones?

I have the following optimization problem: \begin{align}\min&\quad x\\ \text{s.t.}&\quad x=\max_{i} \{x_{i}\}\\ &\quad x_{i}y_{i}=z_{i}\\ &\quad x_{i}, y_{i}, z_{i}\geqslant0 \end{...
PNoug's user avatar
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