I am new to optimization. I have a problem $Y_k=\sum_{m=1}^M x_{mk} log(1+C_{mk})$
$maximize\sum_{k=1}^K{Y_k} $
subject to: $Y_k \geq b, \forall k $
$\sum_{k=1}^K x_{mk}\leq 1, \forall m $
$ 0 \leq x_{mk} \leq 1, \forall m,k$
.
Is this convex optimization problem. How can we show it using first order necessary condition or Hessian matrix? Or is there any other way to show it?