[Ipopt] Options that control the value of mu
Brad Bell
bradbell at seanet.com
Sun Feb 19 15:56:19 EST 2012
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
12 1.9691723e+02 3.31e-04 5.15e+00 -2.7 2.17e-01 - 1.00e+00
8.78e-01h 1
13 1.9754316e+02 2.49e-04 3.16e+01 -2.7 1.39e+00 - 1.00e+00
2.50e-01h 3
14 1.9818965e+02 2.51e-04 3.16e+01 -2.7 1.12e+00 - 1.00e+00
2.50e-01h 3
15 2.0326698e+02 2.38e-04 3.16e+01 -2.7 7.36e-01 - 3.99e-01
1.00e+00H 1
16 2.0756761e+02 1.41e-04 4.30e+01 -2.7 2.77e-01 - 6.27e-01
1.00e+00H 1
17 2.1225000e+02 2.33e-04 2.27e-01 -2.7 1.63e-01 - 1.00e+00
1.00e+00H 1
18 2.1412225e+02 1.50e-04 5.02e-02 -3.3 1.22e-01 - 1.00e+00
1.00e+00h 1
19 2.1637687e+02 5.51e-05 3.67e+00 -4.0 1.98e-01 - 1.82e-01
8.65e-01h 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du
alpha_pr ls
20 2.1642148e+02 5.51e-05 1.96e+00 -4.0 1.31e+00 - 1.98e-01
1.56e-02h 7
21 2.1646676e+02 5.53e-05 9.60e-01 -4.0 1.58e+00 - 4.09e-01
1.56e-02h 7
22 2.1651160e+02 5.55e-05 2.46e+00 -4.0 1.46e+00 - 3.57e-01
1.56e-02h 7
23 2.1655600e+02 5.55e-05 3.39e+00 -4.0 1.36e+00 - 3.47e-01
1.56e-02h 7
24 2.1660010e+02 5.54e-05 4.67e+00 -4.0 1.28e+00 - 6.83e-01
1.56e-02h 7
25 2.1664380e+02 5.53e-05 4.82e+00 -4.0 1.20e+00 - 3.21e-01
1.56e-02h 7
26 2.1668729e+02 5.51e-05 5.31e+00 -4.0 1.14e+00 - 1.00e+00
1.56e-02h 7
27 2.1673041e+02 5.48e-05 5.25e+00 -4.0 1.07e+00 - 3.46e-01
1.56e-02h 7
28 2.1681642e+02 5.54e-05 5.22e+00 -4.0 1.03e+00 - 1.00e+00
3.12e-02h 6
29 2.1690138e+02 5.56e-05 5.13e+00 -4.0 9.25e-01 - 4.39e-01
3.12e-02h 6
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du
alpha_pr ls
30 2.1971251e+02 2.26e-03 8.45e-02 -4.0 8.59e-01 - 1.00e+00
1.00e+00w 1
31 2.2195925e+02 1.71e-04 4.66e-02 -4.0 2.08e-01 - 1.00e+00
1.00e+00w 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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