What's the best model to represent this problem solved by YALMIP?

[Salamino15]

I'm using YALMIP to solve this problem.. but how is this be represented/modelled as? e.g. SOCP?

$LOU_{min} = \underset{(m_1,\dots,m_n)\in\mathbb{R}^n}{\text{min}}

 \sum_{i=1}^N - u_i\left(m_i\right)$

$ 0.1 \leq m_i - b_i < p_i \qquad \forall i \in \{1,\dots,n\}$ 

$p_i - m_i \leq rmax_i \qquad \forall i \in \{1,\dots,n\}$

$Q_{req} = \sum_{i=1}^N \left(p_i - m_i\right)$

$u_i(m_i) = {m_i}^{0.5}$ and in other cases ${m_i}^{0.4}$

Thanks! :)

[Johan Löfberg]

In case it is the powers you are asking about, you can use cpower(x,p), and socp models will be derived if possible

https://yalmip.github.io/command/cpower/