line search in gradient descent applied to a convex function I have been working on implementing a line search method for gradient descent where I made an assumption that at any given point on my surface of the loss function I can reach the minima by the single correct value of the learning rate $\eta$ which I should choose. I have been trying to find this learning rate using binary search but after the entire implementation, I came to realize that my assumption I made is wrong which means I cant directly reach my minima from any given point on the surface of the loss function for any given learning rate in a single step. Can I get a more intuitive explanation of why my initial assumption is wrong? 

Edit:  my loss function is convex and has a large number of parameters I am trying to learn ( multidimensional)
This isn't a perfect example but hopefully the idea is clear.
If you start at a point just left of 0, small learning rates will never get it out of the local minimum at the left. But large enough learning rates to leave that local minimum will never let it settle at the global minimum at the right.

A decaying learning rate could work for such a point.