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I would like to transform the following function into its second order cone form but I do not know how to do that $$f_\sigma(s)=\frac{\|s\|_2^2}{\|s\|_2^2+\sigma}$$

Thans a lot if you can help me !

Tito Eliatron
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Romain
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  • If I understand Second-order cone programming, this is an optimization problem with constraints. On your case what are you looking to optimize and under what constraints? – mathcounterexamples.net Nov 11 '20 at 10:51
  • I would like to model this optimisation problem on Julia but I do not know how to express the objective which is the minimisation of$ f_{\sigma}(s)$
    $$ \begin{array}{l}\operatorname{Min} \sum_{i=1}^{I} t_{i} \ \text { s.t. } \quad m_{j}=\Phi \cdot \Psi \cdot \hat{x}{j}, \quad j=1, \ldots, J \ \frac{|\hat{x}|{2}}{|\hat{x}|{2}+\sigma} \leq t{i}, \quad i=1, \ldots, I\end{array} $$     – Romain Nov 11 '20 at 10:59

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