Nice! I admit I don't have a good understanding of the analysis, but if you mean "does repeatedly applying f to some starting point v, like f(f(f(...(v)))) eventually lead to a solution" the answer is definitely not - you can be right next to a solution and not get there by GD or by applying f. My function `iter` applies f over and over, but this was another failed attempt at a solution.

I will endeavour to try your problem, is it related in some way to a well-known problem?