[Ipopt] Objective function decreases extremely slowly

[Ana Maria Barragan Montero]

Dear all,


I am using IPOPT (through Matlab interface) with the option limited memory bfgs hessian approximation to solve a problem of the following characteristics (the total number of variables can change but it is often between 5000 and 10000).


*************************************************************************
This is Ipopt version 3.11.8, running with linear solver ma57.

Number of nonzeros in equality constraint Jacobian...:             0
Number of nonzeros in inequality constraint Jacobian.:    60613
Number of nonzeros in Lagrangian Hessian.............:                 0

Total number of variables............................:                            8659
               variables with only lower bounds:                            8659
     variables with lower and upper bounds:                                  0
               variables with only upper bounds:                                  0
Total number of equality constraints.................:                            0
Total number of inequality constraints...............:                           7
  inequality constraints with only lower bounds:                          7
   inequality constraints with lower and upper bounds:               0
   inequality constraints with only upper bounds:                         0


**************************************************************************


Here below you can find the ipopt options I am using (those which do not appear are set by the program to their default value)


 % Initialization
options.ipopt.bound_frac = 0.01;
options.ipopt.bound_push = 0.001;


options.ipopt.dual_inf_tol     = 1;
options.ipopt.constr_viol_tol  = 0.0001;
options.ipopt.compl_inf_tol    = 0.0001;
options.ipopt.acceptable_constr_viol_tol = 0.01;

% NLP scaling
options.ipopt.nlp_scaling_max_gradient = 100;


% Quasi-Newton
options.ipopt.hessian_approximation = 'limited-memory';
options.ipopt.limited_memory_update_type = 'bfgs';

% Barrier parameter
options.ipopt.mu_strategy = 'monotone';
options.ipopt.mu_init = 0.1;



My problem is that I need a lot of iterations (more than 1500) to get a good result because the objective function (which has a very big value in the beginning) is decreasing extremely slowly. As an example here you have the print output for the iteration 10 and 500:


iter          objective                inf_pr          inf_du      lg(mu)      ||d||       lg(rg)    alpha_du    alpha_pr   ls

 10      5.4760000e+10    0.00e+00     6.20e+02    -0.2     3.33e+02    -         6.13e-02   1.23e-02f    1   sigma=1.00e-06 qf=13Ws


 500   2.9078333e+10    1.38e+10      1.00e+00    -2.9     9.18e+13    -         4.66e-09    3.06e-10f   1  sigma=6.04e-01 qf=12Wp



I wonder if I could use any other ipopt options to make the objective function decrease faster so that I can reduce the number of iterations. Moreover, I am using ma57 solver, do you recommend me any other (as PARDISO for example) for large problems as this one?

I guess that it is normal that the program takes longer at the beginning to find the good search direction since it does not have the information about the hessian because I am using the bfgs approx. In my case I have the information to calculate analytically the hessian. To calculate it at each iteration would increase considerably the computation time, however, I could calculate it at the beginning and thus initialize the hessian to the right value. Do you think that would reduce the number of iterations?


I am new with IPOPT and I don't have much experience in the field of optimization so please let me know if you need more information about my problem (formulation, variables, etc..) that can help you to find a solution.


Thank you in advance,


Ana


________________________________
Ana María Barragán Montero,
PhD student
Université catholique de Louvain
Molecular Imaging, Radiotherapy and Oncology (MIRO)
Avenue Hippocrate 54
B-1200 Bruxelles, Belgium
ana.barragan at uclouvain.be
+32(0) 27649527
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