[Ipopt] Options that control the value of mu
Brad Bell
bradbell at seanet.com
Mon Feb 20 07:44:00 EST 2012
Thanks for the explanation `Note that sometimes mu is decrease more
than once in one iteration (e.g., between iteration 3 and 4 above),
because the barrier problem error is small.'
For my case in question below the values of log10(mu) between iterations
were-.3 and -1.5.
Using the debugger for that case, and stopping at line 227 in
https://projects.coin-or.org/Ipopt/browser/stable/3.10/Ipopt/src/Algorithm/IpMonotoneMuUpdate.cpp
The original value of mu was .5 (directly after the output for iter=8),
the first value of new_mu was .5^2, the second .5^3, the third .5^4, and
the fourth was .5^5.
Note that log10(.5) = -0.30103 and log10(.5^5) = -1.505 which agrees
with the trace output to the accuracy printed.
P.S.
Tracing with the debugger also revealed that the parameter
barrier_tol_factor (which is called kappa_epsilon in the paper) is also
an important consideration in this regard.
Brad
On 02/19/2012 09:20 PM, Andreas Waechter wrote:
> Hi Brad,
>
> I cannot reproduce your observation. For the options
>
> mu_init 0.5
> mu_linear_decrease_factor 0.5
> mu_strategy monotone
> mu_superlinear_decrease_power 1.1
> tol 0.001
>
> I got this on the HS100 problem:
>
> iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du
> alpha_pr ls
> 0 7.1400000e+02 0.00e+00 7.80e+00 -0.3 0.00e+00 - 0.00e+00
> 0.00e+00 0
> 1 7.0995093e+02 0.00e+00 7.68e+00 -0.3 1.09e+02 - 9.18e-01
> 1.56e-02f 7
> 2 6.7901631e+02 3.02e+00 6.38e+00 -0.3 1.45e+02 - 1.00e+00
> 1.79e-01f 1
> 3 6.7946712e+02 1.83e+00 2.25e+00 -0.3 4.28e+00 - 1.00e+00
> 7.19e-01h 1
> 4 6.8093385e+02 0.00e+00 9.10e-01 -0.9 3.54e+00 - 1.00e+00
> 1.00e+00h 1
> 5 6.8065537e+02 4.19e-01 1.22e+00 -1.2 1.83e+00 - 1.00e+00
> 1.00e+00h 1
> 6 6.8073733e+02 0.00e+00 2.18e-01 -1.2 4.19e-01 - 1.00e+00
> 1.00e+00h 1
> 7 6.8066042e+02 0.00e+00 1.21e-02 -1.8 2.51e-01 - 1.00e+00
> 1.00e+00h 1
> 8 6.8063205e+02 0.00e+00 3.67e-05 -3.0 6.90e-02 - 1.00e+00
> 1.00e+00h 1
> 9 6.8063013e+02 0.00e+00 1.33e-07 -4.4 4.36e-03 - 1.00e+00
> 1.00e+00h 1
>
> This coincides with your formula. Note that sometimes mu is decrease
> more than once in one iteration (e.g., between iteration 3 and 4
> above), because the barrier problem error is small.
>
> Regards,
>
> Andreas
>
> On 02/19/2012 02:56 PM, Brad Bell wrote:
>> I am having some trouble understanding the Ipopt optionss that
>> control the value of mu during optimization. According to equation
>> (7) of the reference:
>> `On the implementation of an interior-point filter line-search
>> algorithm for large-scale nonlinear programming'
>> we have
>> mu_{j+1} = max { epsilon/10 , min [ kappa mu_j , mu_j^theta ] }
>>
>> In the Ipopt trace below, it seems that kappa is the linear scaling
>> factor and theta is the superlinear scaling factor. The initial mu =
>> .5 and corresponding log10(mu) = -.3 which agrees with iter = 0 in
>> the trace below.
>>
>> The problem is at iter = 8, the
>> log10(mu_j) = -.3, i.e., mu_j = 0.5
>> log10(mu_{j+1) = -1.5, i.e., mu_{j+1} = 0.032
>> But the value of kappa=.5 and the value of theta=1.1 and so the value
>> of mu_{j+1} should be
>> min[ .5 * .5 , .5^1.1 ] = min[ .25 , .467 ] = .25
>> so the conclusion is that mu_{j+1} = .032 >= .25 which is false.
>>
>> Can someone explain what is going on here ?
>>
>>
>> List of user-set options:
>>
>> Name Value used
>> hessian_approximation = exact yes
>> max_iter = 50 yes
>> mu_init = 0.5 yes
>> mu_linear_decrease_factor = 0.5 yes
>> mu_strategy = monotone yes
>> mu_superlinear_decrease_power = 1.1 yes
>> nlp_lower_bound_inf = -1e+19 yes
>> nlp_upper_bound_inf = 1e+19 yes
>> print_level = 5 yes
>> print_user_options = yes yes
>> tol = 0.001 yes
>> This is Ipopt version 3.10, running with linear solver mumps.
>>
>> Number of nonzeros in equality constraint Jacobian...: 3904
>> Number of nonzeros in inequality constraint Jacobian.: 0
>> Number of nonzeros in Lagrangian Hessian.............: 17012
>>
>> Total number of variables............................: 750
>> variables with only lower bounds: 0
>> variables with lower and upper bounds: 750
>> variables with only upper bounds: 0
>> Total number of equality constraints.................: 380
>> 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 1.7336986e+03 9.06e-01 9.76e+01 -0.3 0.00e+00 - 0.00e+00
>> 0.00e+00 0
>> 1 7.3646697e+02 2.98e-01 6.25e+02 -0.3 1.46e+00 2.0 4.12e-01
>> 9.95e-01f 1
>> 2 6.1674749e+02 2.71e-01 7.48e+02 -0.3 6.53e+00 1.5 2.32e-01
>> 8.95e-02f 1
>> 3 5.5840255e+02 2.15e-01 6.11e+02 -0.3 2.43e+00 - 3.46e-02
>> 2.03e-01f 1
>> 4 3.3685504e+02 1.42e-01 3.55e+02 -0.3 1.10e+00 - 1.83e-01
>> 4.21e-01f 1
>> 5 1.9885799e+02 9.32e-02 5.83e+01 -0.3 8.30e-01 - 7.44e-01
>> 9.90e-01f 1
>> 6 2.0559440e+02 1.41e-01 1.11e+04 -0.3 1.05e+00 - 3.31e-01
>> 1.00e+00f 1
>> 7 1.9305692e+02 5.79e-02 4.31e+03 -0.3 3.53e+00 - 4.83e-01
>> 7.42e-01h 1
>> 8 1.8984018e+02 1.82e-02 1.51e+00 -0.3 1.06e+00 - 1.00e+00
>> 1.00e+00f 1
>> 9 1.9125490e+02 4.80e-03 1.11e+02 -1.5 4.82e-01 - 6.92e-01
>> 9.99e-01H 1
>> iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du
>> alpha_pr ls
>> 10 1.9256817e+02 3.67e-03 1.06e-01 -1.5 4.53e-01 - 1.00e+00
>> 1.00e+00h 1
>> 11 1.9468436e+02 1.58e-03 3.03e+00 -2.7 4.07e-01 - 9.53e-01
>> 8.80e-01h 1
>> [...]
>> 32 2.2479027e+02 1.12e-04 7.42e-02 -4.4 1.52e-01 - 1.00e+00
>> 1.00e+00h 1
>> 33 2.2749869e+02 8.63e-05 6.49e-02 -4.4 1.29e-01 - 1.00e+00
>> 1.00e+00h 1
>> 34 2.3009148e+02 5.67e-05 5.57e-02 -4.4 1.00e-01 - 1.00e+00
>> 1.00e+00h 1
>>
>> Number of Iterations....: 34
>>
>> (scaled) (unscaled)
>> Objective...............: 2.3009147704253428e+02
>> 2.3009147704253428e+02
>> Dual infeasibility......: 5.5729744609665358e-02
>> 5.5729744609665358e-02
>> Constraint violation....: 5.6684216535626365e-05
>> 5.6684216535626365e-05
>> Complementarity.........: 3.9139910972968873e-05
>> 3.9139910972968873e-05
>> Overall NLP error.......: 7.9497813272578718e-04
>> 5.5729744609665358e-02
>>
>>
>> Number of objective function evaluations = 126
>> Number of objective gradient evaluations = 35
>> Number of equality constraint evaluations = 126
>> Number of inequality constraint evaluations = 0
>> Number of equality constraint Jacobian evaluations = 35
>> Number of inequality constraint Jacobian evaluations = 0
>> Number of Lagrangian Hessian evaluations = 34
>> Total CPU secs in IPOPT (w/o function evaluations) = 1.517
>> Total CPU secs in NLP function evaluations = 246.303
>>
>> EXIT: Optimal Solution Found.
>>
>> _______________________________________________
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>
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