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<p>Dear all, </p>
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<p>I am using IPOPT (through Matlab interface) with the option <em>limited memory bfgs hessian approximation</em> to solve a problem of the following characteristics (the total number of variables can change but it is often between 5000 and 10000).
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<p>*************************************************************************<br>
This is Ipopt version 3.11.8, running with linear solver ma57.<br>
<br>
Number of nonzeros in equality constraint Jacobian...: 0<br>
Number of nonzeros in inequality constraint Jacobian.: 60613<br>
Number of nonzeros in Lagrangian Hessian.............: 0<br>
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Total number of variables............................: 8659<br>
variables with only lower bounds: 8659<br>
variables with lower and upper bounds: 0<br>
variables with only upper bounds: 0<br>
Total number of equality constraints.................: 0<br>
Total number of inequality constraints...............: 7<br>
inequality constraints with only lower bounds: 7<br>
inequality constraints with lower and upper bounds: 0<br>
inequality constraints with only upper bounds: 0</p>
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<p>**************************************************************************<br>
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<p>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)</p>
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<p> % Initialization<br>
options.ipopt.bound_frac = 0.01; <br>
options.ipopt.bound_push = 0.001;</p>
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<p>options.ipopt.dual_inf_tol = 1; <br>
options.ipopt.constr_viol_tol = 0.0001; <br>
options.ipopt.compl_inf_tol = 0.0001; <br>
options.ipopt.acceptable_constr_viol_tol = 0.01; <br>
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% NLP scaling<br>
options.ipopt.nlp_scaling_max_gradient = 100; <br>
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<p>% Quasi-Newton<br>
options.ipopt.hessian_approximation = 'limited-memory'; <br>
options.ipopt.limited_memory_update_type = 'bfgs';<br>
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% Barrier parameter<br>
options.ipopt.mu_strategy = 'monotone';<br>
options.ipopt.mu_init = 0.1; <br>
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<p>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:</p>
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<p>iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls<br>
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<p> 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</p>
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<p> 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</p>
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<p>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? </p>
<p>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?
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<p>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.</p>
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<p>Thank you in advance, </p>
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<p>Ana<br>
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