I am trying to find the minimizer of the function

s.t. , if

We use the function

we have that

So we can actually solve the problem

Minimize

s.t.

Now my reasoning is, by letting , the problem becomes:

Minimize i.e. Minimize

or Minimize

Now, I think I should first find the critical points for the function . But, should I consider this function as a function of and , or as a function of and ?

Another way of thinking about this problem. If I use the 'Fischer-Burmeister' function which is:

I am trying to find the minimizer of the function

s.t. , if

We use the function

we have that

So we can actually solve the problem

Minimize

s.t.

Now my reasoning is, by letting , the problem becomes:

Minimize i.e. Minimize

or Minimize

Now, I think I should first find the critical points for the function . But, should I consider this function as a function of and [itex]g[/TEX], or as a function of and ?

Another way of thinking about this problem. We can use the 'Fischer-Burmeister' function which is:

instead of the function because for the 'Fischer-Burmeister' function,

just like for the previous function .

Now, the problem would be to

Minimize .

Again, how should I go about finding this minimum?