bad convergence of steepest descent

Question

Under which circumstances does the steepest descent method converge badly?

I know if the search direction is approximately perpendicular to the descent direction the steepest descent method converges slowly.

What other situations are there in which the method converges slowly and/or badly?

Answer 1

Classic example would be $$f(x, y) = \alpha x^2 + \beta y^2 $$ with $\beta \gg \alpha > 0$. Then, the contours are stretched (in $x$) ellipsoids and the steepest descent method converges slowly.