[Ipopt] Questions

[Michele Castellana]

Dear Ipopt users,
Thank you for replying to my former question about the use of Ipopt without supplying the gradient of the objective function. 
I have another two questions that you may be able to help me with. Given that I want to minimize an objective function f(x_1, ..., x_N) with some inequality constraints, suppose that the gradient \partial f / \partial x_i is such that | \partial f / \partial x_i | is a decreasing function of i, e. g. the objective function strongly depends on the first variables and the larger i the weaker the dependence of f on x_i. In my case typically N ˜ 30 and | \partial f / \partial x_i | ˜ C^{-i}, where C > 1 is a number. Can Ipopt deal with this kind of problems? Might there be some issues related to the presence of 'hard' and 'soft' variables?

My second question is the following: if the objective function has local minima, can Ipopt escape the local minima or it will get stuck there anyway? If it has some strategy for escaping local minima, where can I find some example? 

Thank you very much for your help!
Best
Michele