[Ipopt] Can i use IPOPT without the input of Jacobian Matrix and the Hessian of the Lagrangian?

[Uwe Nowak]

> I do not have a clear concept on optimization.
> Do there have any big difference between the default method than the quasi-newton approx. of second derivatives?
> Will it decrease the accuracy of result? or it will only increase the number of iteration?

This is dependent on the problem, but usually using approximation of 
second order derivatives
- leads to faster computations per iteration
- increases the number of iterations to converge
- may lead to convergence problems for some instances


If your problem is not to ill conditioned or to big, the quasi newton 
approximations are reasonable. It is not a hack, is is a serious, well 
developed algorithm with a lot of theory about it. If there are no 
second order derivatives, it is the best you can do.

So you can use it. It should work. And if you find your algorithm is to 
slow or has convergence problems, you still might try exact Hessians.