[Ipopt] Objective value trouble

Sebastian Ferrera Ferrera sebastian.ferrera at corpbanca.cl
Fri Dec 10 09:13:06 EST 2010

Hi Stefan,

You are right, I am using the same boundary condition on x twice: first as -10 < x < 10 and then as -10 < f(x) = x < 10 (jacobian = 1). There is only one variable x.


-----Mensaje original-----
De: Stefan Vigerske [mailto:stefan at math.hu-berlin.de] 
Enviado el: Viernes, 10 de Diciembre de 2010 10:51
Para: Sebastian Ferrera Ferrera
CC: ipopt at list.coin-or.org
Asunto: Re: [Ipopt] Objective value trouble


it seems to work for me. Using the attached gams model, Ipopt has no problem to find the optimal solution, see output below.

What puzzles me, is that even though you have an unconstrained minimization problem (except for the variable bounds), the Ipopt statistics in your output mention one inequality constraint, but still only one variable. So what exactly are the objective and constraints that you give to Ipopt?

And yes, and as in Jeff's mail, x=-1 is the solution, not x=-1/2.


Number of nonzeros in equality constraint Jacobian...:        0
Number of nonzeros in inequality constraint Jacobian.:        0
Number of nonzeros in Lagrangian Hessian.............:        1

Total number of variables............................:        1
                     variables with only lower bounds:        0
                variables with lower and upper bounds:        1
                     variables with only upper bounds:        0
Total number of equality constraints.................:        0
Total number of inequality constraints...............:        0
        inequality constraints with only lower bounds:        0
   inequality constraints with lower and upper bounds:        0
        inequality constraints with only upper bounds:        0

iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du
alpha_pr  ls
   0  1.5000000e+00 0.00e+00 2.00e+00   0.0 0.00e+00    -  0.00e+00
0.00e+00   0
   1 -4.4350687e-01 0.00e+00 5.53e-02  -5.0 1.66e+00    -  8.36e-01
1.00e+00f  1
   2 -4.9994384e-01 0.00e+00 5.03e-17  -1.9 3.26e-01    -  1.00e+00
1.00e+00f  1
   3 -5.0000000e-01 0.00e+00 4.76e-05  -3.4 1.06e-02    -  9.96e-01
1.00e+00f  1
   4 -5.0000000e-01 0.00e+00 7.21e-08  -9.1 2.30e-05    -  9.99e-01
1.00e+00f  1
   5 -5.0000000e-01 0.00e+00 3.37e-17 -11.0 3.95e-10    -  1.00e+00
1.00e+00f  1

Number of Iterations....: 5

                                   (scaled)                 (unscaled)
Objective...............:  -5.0000000000000000e-01   -5.0000000000000000e-01
Dual infeasibility......:   3.3699894020781983e-17    3.3699894020781983e-17
Constraint violation....:   0.0000000000000000e+00    0.0000000000000000e+00
Complementarity.........:   1.0000045988089869e-11    1.0000045988089869e-11
Overall NLP error.......:   1.0000045988089869e-11    1.0000045988089869e-11

Number of objective function evaluations             = 6
Number of objective gradient evaluations             = 6
Number of equality constraint evaluations            = 0
Number of inequality constraint evaluations          = 0
Number of equality constraint Jacobian evaluations   = 0
Number of inequality constraint Jacobian evaluations = 0
Number of Lagrangian Hessian evaluations             = 5
Total CPU secs in IPOPT (w/o function evaluations)   =      0.020
Total CPU secs in NLP function evaluations           =      0.000

EXIT: Optimal Solution Found.

> I am currently working on a project using the IPopt minimization under contraints.
> An example for visual studio "csipopt" converges successfully.
> Yet - for the sake of benchmarking - I am trying to minimize the 1D polynomial f(x) = x + x2/2 under the constraints -10<x<10 and with initial guess x = 1.
> Accordingly the gradient is g(x) = 1 + x and the hessian h(x) = 1. IPopt fails to find the minimum x=-1/4 as the iterations deviate only marginally from the initial value as shown by the attached file.
> Please advise me how to proceed. I suspect this must be a minor option setting.
> Thank you.
> Sebastian Ferrera, Chile
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Stefan Vigerske
Humboldt University Berlin, Numerical Mathematics http://www.math.hu-berlin.de/~stefan

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