[Coin-ipopt] hessian information for optimal control problems

[Andreas Waechter]

Hi Saeed,

Since the limited memory quasi-Newton options are not that robust, I
suggest that you implement the evaluation of the Hessian matrix for your
problem if possible - if you differential equations f are given
analytically, this is probably not too difficult.  (In general, I would
always recommend to use second derivative information if available, and if
the Hessian matrix is not dense.)

I'm not sure what exactly you are asking regarding the Hessian.  The fact
that you have solving an optimal control problem doesn't change its general
definition for a nonlinear optimization problem:

Your problem formulation has a number of variables x_i (e.g. your
disretized states), say n, and constraints (such as the discretized
differential equation), i.e. you have

c_i(x)

as a function from R^n to R for each equality constraint c_i.  You also
have an objective function f(x):R^n -> R.

The Hessian of the Lagrangian function is computed from

W = (Hessian of f) + sum_i ( lambda_i * (Hessian of c_i) )

where the Hessian matrices are computed at a given point x, and the
lambda's are weighting factors (X and LAM in the definition of eval_h).

I hope this helps,

Andreas



                                                                                                                                                    
                      saeed serpooshan                                                                                                              
                      <sserpooshan at yahoo.com>         To:       coin-ipopt at list.coin-or.org                                                         
                      Sent by:                        cc:                                                                                           
                      coin-ipopt-bounces at list.        Subject:  [Coin-ipopt] hessian information for optimal control problems                       
                      coin-or.org                                                                                                                   
                                                                                                                                                    
                                                                                                                                                    
                      12/27/2004 03:55 AM                                                                                                           
                                                                                                                                                    
                                                                                                                                                    




hi
i'm very happy that see you reply my questions.. this is very good! thanks
i have a question about using ipopt for solution of an optimal control
problem. i want to use my own code to discretize optimal control problem
and convert it to NLP such that ipopt can solve it. for this, i use
trapezoidal rule to convert differential equations of dynamic system into
discrete form as a series of equality constraints: c(i,k) = x(i,k+1) -
x(i,k) - h* (f(i,k)+f(i,k+1))/2  where i=[1..nx] number of states and k is
index for time grid [1..nt-1]
i find derivativ of these equations analytically because it is simple. i
use ipopt with options IFull=1 and IQUASI=6 such that hessian is not
required by me. this approch works fine for some simple problems. (for
example for an min-energy problem in bryson-ho, x(0)=x(1)=0, v(0)=1=-v(1) ,
minimize f=1/2*u^2 with a path constraint x<1/9 IPOPT Converges in only 11
iterations with exact solution)
but now i want to solve shuttle ReEntry problem as in NEOS Server samples
solved by ipopt.
for that complicate problem my approch not converged at all. i am not sure
why? is it because of lack of hessian information? how can i find that for
an optimal control problem? can you help me?

thanks
s.serpooshan




__________________________________________________
Do You Yahoo!?
Tired of spam? Yahoo! Mail has the best spam protection around
http://mail.yahoo.com _______________________________________________
Coin-ipopt mailing list
Coin-ipopt at list.coin-or.org
http://list.coin-or.org/mailman/listinfo/coin-ipopt