Which numerical methods would be optimal to find an extremum of a function with an almost flat "valley" (but a single minimum in the middle of the valley)? In this context optimal means the least number of function evaluations.
For simplicity's sake, assume that it's a two-dimensional problem. Also, of importance may be that I am more interested not in the coordinates of the extremum, but the value of the function in it.
For reference, the Rosenbrock function is $$f(x,y) = (1-x)^2 + 100(y-x^2)^2$$
I am using the term "'Rosenbrock'-like", because I have not yet defined the function itself. The problem I am solving is that of nonlinear equality constraint optimization, which I believe I have reduced to a global optimization of a function with a "valley" along the constraint.