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)