What are Fletcher-Reeves and the Wolfe inexact line search?

Question

I need to implement the Fletcher-Reeves conjugate gradient method with the Wolfe inexact line search to find the stationary point of

$$S(y) =20 \sum_{i=1}^9 ( 1 + y_{i+1} - y^2_{i} - y_i)^2$$

While googling Fletcher-Reeves method, I found the following iterative algorithm on wikipedia. My concern is that I don't really understand, what the Wolfe inexact line search is. Also, I cannot get what $A$ and $b$ are for my function.

Any advice is welcome.

Answer 1

For what it's worth, you can find a working Wolfe line search in the scipy source code. There is also a BFGS algorithm if you want.