I want to be very clear about these algorithms in a paper I'm writing. In the documentation BRENT is said to be a variation of a golden section method described in Brent (1972). I have the 2002 reissue. Are we talking about Chapter 5.4? The algorithm described is a mixture of golden section and parabolic steps. Is that the one? I wish I remembered some ALGOL which I studied (poorly) in 1964 or 1965.
STEPBT references Dennis and Schnabel. "BT" stands for backtrack I am inferring from the module called LINESEARCH in Algorithm A6.3.1. Is that it?
I am working on ML estimation of the Generalized Beta 2 distribution. It has only 4 parameters but the ML problem is made difficult by ill-conditioning when p is about equal to q. Algorithm choice turns out very important.
Thanks,
Carter Hill-
1 Answer
0
You could change B(p,q) to B(q+sqrt((d + delta)^2),q) redefining p = q + d, and in your function set where delta is fixed to some small number, 1e-4, say. This is a differentiable way of constraining p - q to be greater than that small number.
Alternatively SQPsolvemt or CMLmt could be used to constrain p - q to be greater than a small number.
I am not sure about the algorithm. I will see who I can ask about that.
Your Answer
1 Answer
You could change B(p,q) to B(q+sqrt((d + delta)^2),q) redefining p = q + d, and in your function set where delta is fixed to some small number, 1e-4, say. This is a differentiable way of constraining p - q to be greater than that small number.
Alternatively SQPsolvemt or CMLmt could be used to constrain p - q to be greater than a small number.
I am not sure about the algorithm. I will see who I can ask about that.