When i have this problem:
$min f(x)$
$h{_i}(x)=0, i=1,\dots,m$
$g{_j}(x)<=0, j=1,\dots,p$
I can use the Lagrangian multiplier to write function in:
$L(x,\lambda,\mu)=f(x)+\sum_{i=1}^{m} \lambda{_i}h{_i}(x)+\sum_{j=1}^{p} \mu{_j}g{_j}(x)$.
Why can I write this, in this form : $L(x,\lambda,\mu)=f(x)+\lambda^T h(x)+\mu^Tg(x)$ ? I don't understand because i can substituite the sum with $\lambda^T$ and $\mu^T$.