[Coin-ipopt] fixed variables question

saeed serpooshan sserpooshan at yahoo.com
Mon Feb 28 03:49:18 EST 2005

hi dear andreas
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 with
 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. 
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
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.

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