# How to check optimality for a solution from convex+monotonic objective function

I have a objective function like

 min_x c(x) + m(x)  s.t x >= 0


c(x) is a differentiable convex function, and m(x) is a monotonic increasing function (linear or non-linear), but non-differentiable.

I also found a solution of the objective function, but I don't know how this can be shown that my solution is optimal (at least local minima. If global optimality, better).

Is there any related literature of this kind of problem?? or any theory for this kind of objective function (like concave-convex procedure).

I want to find any reference to prove it has global optimal (It seems to be).

If general optimality theory doesn't exist, please let me know it is.