This is not a typical question with a deterministic answer. If this is not the right place, feel free to close it.
For the past one year I have been working on various kinds of inverse problem. Most of them are related to parameter estimation, ranging from small linear differential equation to equations of fluid dynamics. And consistently, I observed that it was easier to find a solution to the non linear problem(using same optimization method, let's say steepest descent). By easy I mean it requires lower number of iterations for the same decrease(very subjective). Although, it is nearly impossible to compare different cases exactly, this trend is surprising to me.
The question here is, did anyone else observe similar behaviour? Is there a qualitatively explanation for this behaviour?
This also raises a follow up question of whether we can quantify(from the initial jacobian may be?) the level of difficulty involve in finding a solution?(or estimate the order of magnitude of the number of optimizer steps)