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?