[Coin-ipopt] fixed variables question

Lorenz T Biegler lb01 at andrew.cmu.edu
Mon Feb 28 22:22:28 EST 2005

Dear Saeed

many thanks for the message. Perhaps I can help with a response.

> first, thanks for your interest and responsibility again
> my problem is a optimal control with severall stages. we don't have any 
> control in stage 4 i.e. it is a free flight (without thrust force) that 
> use last states at end of stage 3 and going us to begining of stage 5. i 
> have my own code and don't use ampl. my code convert problem to 
> non-linear-programming such that it can be solved by ipopt. because of 
> some simplification all stages trated same manner in this conversion so 
> i have some variables that are not any effect on anything, i.e. controls 
> at stage 4 do not have any meaning when thrust is zero. when i solve 
> only first 3 stages the problem has relatively good convergence and 
> solution is almost acceptable. but when i add stage 4 the KKT error 
> becomes grate and very oscillated and don't let solution progress (mu 
> remain 0.1). i think that it may be because of those control variables 
> that don't have any effect on cost function F and ipopt don't know how 
> should change them to improve optimality error. so i fix those variables 
> wi! th Lower/Upper bounds both to zero. in this case the problem has 
> better convergence but still have problems: mu is not going lower than 
> E-06 and answers are relatively different when i change number of grids.

Because the problem is written with your own code, I think it would be 
difficult to isolate the difficulty with the additional stage constraints. 
First, it is important that accurate first and, if possible, second 
derivates be supplied to IPOPT; this is crucial to successful convergence 
and good performance. This is one reason to use AMPL to model your 
problem, as these issues are handled in a straightforward manner. It 
sounds like the addition of the fourth stage could be leading to 
difficulties in the derivatives.

Also, that the small bounds seemed to help might be an indication of the 
derivative problem.

> can you state more about fixed vars or something else that may help me 
> for this problem?
> i know that ipopt remove fixd vars from list of real NLP variables but 
> it seems that it is not as robust as usuall problems when number of 
> those fixed vars are not small

the fixed vars does remove these variables. However, this could lead to 
other problems as the resulting constraints with these variables removed 
could be degenerate.

> also, i know one way is to modify my code such that stage 4 be omitted 
> from NLP problem but because it can't be found analytically (or very 
> complicated), one must integrate a 600...1500 second of some 
> differential equations as an ODE to find final states of stage 4 as 
> initial conditions of stage 5 and this is expensive if it repeated for 
> each iteration.

This may be useful. Let me also suggest that it may be possible to 
discretize the differential equations (using e,g. a runge-kutta 
discretization) and add them as constraints to the 
IPOPT model directly. This can be done, for example, in AMPL.

Hope this helps

Larry Biegler

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