Why do we need f in project_gradient_descent?

[aiwen324]

Do we have to find the smallest value? Say if we achieve the minimum at 50th iter then we should assign the z-value at 50th iter instead of z in the last iter?

[abhimadan]

The f is used when determining the step size in the line search. The heuristic we're using here is that we want each gradient descent step to decrease f, so we use line search to make sure that we're actually doing this, while also avoiding unnecessarily small steps that will make us take a long time to reach a local minimum.