[Ipopt] Questions on "Total CPU secs in NLP function evaluations"

[Tony Kelman]

1. Yes, you’re correct that NLP function evaluations means objective, gradient, Jacobian, and Hessian functions. These are considered user-defined functions, although when using the AMPL interface to Ipopt it is that AMPL interface code that is responsible for evaluating these functions. The inside-Ipopt time is primarily the time spent in the linear solver (ma27 in your example data), solving the KKT system to determine the Newton step at each iteration, potentially multiple times per iteration if Hessian regularization is required, then a bit more cheap math for the line search. You can get a more detailed breakdown of where the time is being spent by setting the option print_timing_statistics to yes.

2. Conceptually these should be parallelizable since it’s just function evaluation and each element of the vector and sparse matrix quantities only depends on the current primal-dual evaluation point, not the other vector/matrix elements. Since you’re using the AMPL interface I’m not sure how easy this is to implement in practice. I don’t believe the AMPL interface code is written in a way that could be easily parallelized, but I could be wrong here. How complicated would your problem be to implement in C++ or something you have more control over? I believe some of the auto-differentiation tools should support some form of parallel evaluation?

I find it a bit surprising to see an AMPL model taking almost 4 times longer in the function evaluations than the linear solver, I usually expect the linear solver time to dominate for most problems (unless you’re using an interface like Matlab or Python where the user functions might be written as slow interpreted code). Does your problem have a large number of complicated nested nonlinearities or discontinuities or something else that may be giving AMPL trouble? Look at the more detailed timing statistics to see which of the functions is taking most of the time, if the Hessian is taking an inordinate amount of time you could try the quasi-Newton limited-memory Hessian option by setting the hessian_approximation option to limited-memory. Otherwise is there any type of reformulation you could do, potentially introducing more variables but making the problem sparser or consolidating some of the more difficult nonlinearities into fewer variables or constraint elements?

-Tony


From: Yao Xie 
Sent: Tuesday, October 01, 2013 1:43 PM
To: ipopt at list.coin-or.org 
Subject: [Ipopt] Questions on "Total CPU secs in NLP function evaluations"

Hi all, 

I couldn't find documentation to explain the difference of "Total CPU secs in IPOPT (w/o function evaluations)" and "Total CPU secs in NLP function evaluations". I was using AMPL interface and got a very long function evaluation time (details below).

My questions are:
1) What's the difference between these two CPU time? Does "NLP function evaluations" mean to evaluate objective function values, Jacobian, Hessian matrix? Which parts are in IPOPT and which are outside IPOPT?
2) Is there any way to speed up this NLP function evaluation part? It's just evaluation, can we parallelize it? Thanks!

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