How to jump-start with mathnet as a novice?

I have a concrete problem to solve. However, I have difficulty to start with MathNet Minimization.
I learned to use the Maxtrix stuff. But the Minimization facilities baffle me.
Let me be concrete:
I have a C# method f for which I need to find a minimum. The method describes a catenary, with a few vertical loads. (so not a clean cosh-function, but an irregularly rising and decreasing one ). The signature looks like

double f(Vector v);

in which v is a 2-element vector, representing initial values (a 2D minimization). The return value must approach zero.

I understand that I must choose a minimizer (eg. NewtonMinimizer?), and have an “ObjectiveFunction”.
Questions: what is an ObjectiveFunction and why is it “Objective”?
Is it something like my f method? and how would I build one from f, if yes?
From what i descibed above, can I define a gradient function? (Some minimizers need one). Or do I need one at all?
Are there complete , commented and detailed examples to be found anywhere on the net?