使用 GEKKO MHE 时的方程定义错误（没有等式或不等式的方程）
Equation Definition Error (Equation without an equality or inequality) while using GEKKO MHE
我目前正在试用 GEKKO MHE 模式。我在模型中有两个指定的操纵变量和控制变量，以及一个我希望通过 MHE 估计的参数。当我当前 运行 模型时，我得到一个方程定义错误，说
没有等式 (=) 或不等式 (>,<) 的方程式
-267.25544516-267.28925105-267.21324717-267.21191109-264.56454462
正在停止...
模型初始化为：
from gekko import GEKKO
import numpy as np
import matplotlib.pyplot as plt
import pandas as pd
n = 17
m = GEKKO(remote=False)
m.time = np.linspace(0,8,n)
c1_in_arr = np.load('c1_in_arr.npy')
c2_in_arr = np.load('c2_in_arr.npy')
V1_measured = np.load('V1_measured.npy')
V2_measured = np.load('V2_measured.npy')
#mmanipulated variables, feeding in the arrays for them
m.C1_in = m.MV(value=c1_in_arr)
m.C2_in = m.MV(value=c2_in_arr)
#estimated variables, feeding in the upper and lower bounds for them
m.C1_eff = m.FV(value = 0.98, lb = 0.95, ub = 1.0)
#controlled variables, feeding in the measurements for them
m.V1 = m.CV(value=V1_measured)
m.V2 = m.CV(value=V2_measured)
mdot_1 = m.Var()
mdot_2 = m.Var()
m.Equation(mdot_1== 1.52*m.C1_eff*m.C1_in)
m.Equation(mdot_2==-0.668*mdot_1 + 1.33*m.C1_eff*m.C2_in)
df_c = pd.read_csv('Values_C.csv',index_col=0)
Hhat_C1 = m.Var()
Hhat_C1 = m.Var()
M_m = 125
mdot_m = 75
mdot_s = 46
m.Equations([Hhat_C1 == -0.606 + 0.0057 * mdot_1,
Hhat_C2 == -3.933 + 0.00096 * mdot_1])
C1_m = m.Var(value = 200)
C2_m = m.Var(value = 150)
m.Equations([C1_m.dt() == mdot_1 - C1_m/M_m*mdot_m,
C2_m.dt() == mdot_2 - C2_m/M_s*mdot_s)
m.Equation(m.V1==0.8*C1_m/M_m)
m.Equation(m.V2 == 0.78*C1_m/C2_m)
m.options.IMODE = 5
#setting the solver settings to MHE
m.options.EV_TYPE = 1
#setting the solver for the MHE to calculate the parameters based on the sum of absolute errors
m.C1_in.STATUS = 0
m.C2_in.STATUS = 0
m.SiO2_in.STATUS = 0
m.C1_eff.STATUS = 1
m.V1.STATUS = 1
m.V2.STATUS = 1
m.C1_in.FSTATUS = 1
m.C2_in.FSTATUS = 1
m.C1_eff.FSTATUS = 0
m.V1.FSTATUS = 1
m.V2.FSTATUS = 1
m.C1_eff.DMAX = 1.0
m.V1.MEAS_GAP = 0.001
m.V2.MEAS_GAP = 0.001
m.open_folder()
m.solve(disp = False)
当我在求解之前打开 GEKKO 文件夹时，文件夹中也不存在不可行性文件。
当将 MV 和 CV 初始化为“测量”数组的第一个变量时，模型能够 运行 没有错误
例如。 m.C1_in = m.MV(值=c1_in_arr[0])
然而，提供的参数估计不正确。
我认为这个错误可能是由于我的 MV 和 CV 在模型中的处理方式所致。有没有办法查明是哪个方程导致了这个错误，或者是由于 MV/CV 初始化造成的？
谢谢！
在 Gekko 方程中使用 Numpy 数组或 Pandas 数据帧可能会出现问题，例如：
# incorrect
df_c = pd.read_csv('Values_C.csv',index_col=0)
m.Equation(m.C1_in==df_c)
您可以通过创建输入参数来解决此错误，例如：
# correct
df_c = pd.read_csv('Values_C.csv',index_col=0)
df_c = m.Param(df_c)
m.Equation(m.C1_in==df_c)
我没有你的 .npy 文件，所以我无法重现你的错误。但是，我确实用长度为 n 的随机数组输入替换了那些以获得成功的解决方案。还有一些未定义的参数，例如 M_s，因此我包含了一些示例值。您对 MVs 和 CVs 的定义很好。该错误可能是由于其他输入参数在方程中使用之前需要转换为 Gekko 类型参数。
from gekko import GEKKO
import numpy as np
import matplotlib.pyplot as plt
import pandas as pd
n = 17
m = GEKKO(remote=False)
m.time = np.linspace(0,8,n)
c1_in_arr = np.random.rand(n)
c2_in_arr = np.random.rand(n)
V1_measured = np.random.rand(n)
V2_measured = np.random.rand(n)
#mmanipulated variables, feeding in the arrays for them
m.C1_in = m.MV(value=c1_in_arr)
m.C2_in = m.MV(value=c2_in_arr)
#estimated variables, feeding in the upper and lower bounds for them
m.C1_eff = m.FV(value = 0.98, lb = 0.95, ub = 1.0)
#controlled variables, feeding in the measurements for them
m.V1 = m.CV(value=V1_measured)
m.V2 = m.CV(value=V2_measured)
mdot_1 = m.Var()
mdot_2 = m.Var()
m.Equation(mdot_1== 1.52*m.C1_eff*m.C1_in)
m.Equation(mdot_2==-0.668*mdot_1 + 1.33*m.C1_eff*m.C2_in)
Hhat_C1 = m.Var()
Hhat_C2 = m.Var()
M_m = 125
M_s = 125
mdot_m = 75
mdot_s = 46
m.Equations([Hhat_C1 == -0.606 + 0.0057 * mdot_1,
Hhat_C2 == -3.933 + 0.00096 * mdot_1])
C1_m = m.Var(value = 200)
C2_m = m.Var(value = 150)
m.Equations([C1_m.dt() == mdot_1 - C1_m/M_m*mdot_m,
C2_m.dt() == mdot_2 - C2_m/M_s*mdot_s])
m.Equation(m.V1==0.8*C1_m/M_m)
m.Equation(m.V2 == 0.78*C1_m/C2_m)
m.options.IMODE = 5
#setting the solver settings to MHE
m.options.EV_TYPE = 1
#setting the solver for the MHE to calculate the
#parameters based on the sum of absolute errors
m.C1_in.STATUS = 0
m.C2_in.STATUS = 0
m.C1_eff.STATUS = 1
m.V1.STATUS = 1
m.V2.STATUS = 1
m.C1_in.FSTATUS = 1
m.C2_in.FSTATUS = 1
m.C1_eff.FSTATUS = 0
m.V1.FSTATUS = 1
m.V2.FSTATUS = 1
m.C1_eff.DMAX = 1.0
m.V1.MEAS_GAP = 0.001
m.V2.MEAS_GAP = 0.001
m.open_folder()
m.solve(disp = True)
如果存在阻止求解器 运行 的模型错误或存在成功的求解，则不会创建文件 infeasibilities.txt。使用随机输入值，有一个成功的解决方案。
----------------------------------------------------------------
APMonitor, Version 0.9.2
APMonitor Optimization Suite
----------------------------------------------------------------
--------- APM Model Size ------------
Each time step contains
Objects : 0
Constants : 0
Variables : 11
Intermediates: 0
Connections : 0
Equations : 8
Residuals : 8
Warning: CV( 1 ) on at cycle 1 with no MVs on
Warning: CV( 2 ) on at cycle 1 with no MVs on
Number of state variables: 417
Number of total equations: - 416
Number of slack variables: - 0
---------------------------------------
Degrees of freedom : 1
**********************************************
Dynamic Estimation with Interior Point Solver
**********************************************
Info: Exact Hessian
******************************************************************************
This program contains Ipopt, a library for large-scale nonlinear optimization.
Ipopt is released as open source code under the Eclipse Public License (EPL).
For more information visit http://projects.coin-or.org/Ipopt
******************************************************************************
This is Ipopt version 3.10.2, running with linear solver mumps.
Number of nonzeros in equality constraint Jacobian...: 510
Number of nonzeros in inequality constraint Jacobian.: 384
Number of nonzeros in Lagrangian Hessian.............: 32
Total number of variables............................: 417
variables with only lower bounds: 192
variables with lower and upper bounds: 33
variables with only upper bounds: 0
Total number of equality constraints.................: 224
Total number of inequality constraints...............: 192
inequality constraints with only lower bounds: 192
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 1.4079997e+001 1.20e+002 9.00e+000 0.0 0.00e+000 - 0.00e+000 0.00e+000 0
1 2.2358394e+002 1.20e+002 9.95e+000 11.0 1.03e+011 - 1.05e-010 1.45e-012f 1
2 3.0439837e+004 1.20e+002 2.27e+005 12.1 1.14e+012 - 2.78e-013 1.89e-011f 1
3 3.0621616e+006 1.20e+002 2.44e+006 11.4 4.33e+010 - 1.00e+000 4.98e-008f 1
4 3.0621722e+006 6.66e-001 2.49e+004 4.6 3.93e+000 - 9.90e-001 1.00e+000f 1
5 3.0609833e+006 1.78e-014 2.55e+002 2.6 1.28e+000 - 9.90e-001 1.00e+000f 1
6 2.9460876e+006 1.42e-014 2.55e+000 0.6 8.89e+001 - 9.90e-001 1.00e+000f 1
7 7.0161757e+005 2.84e-014 2.55e-002 -1.3 1.69e+003 - 9.90e-001 1.00e+000f 1
8 1.1625511e+004 2.84e-014 2.57e-004 -2.7 1.48e+003 - 9.90e-001 9.91e-001f 1
9 1.0176844e+003 6.17e-009 5.69e-002 -0.1 3.45e+003 - 1.00e+000 9.32e-001f 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
10 4.7702371e+002 1.77e-008 3.10e+000 -0.8 8.48e+003 - 1.00e+000 6.38e-001f 1
11 2.8271410e+002 2.82e-007 1.44e+000 -1.0 5.55e+003 - 1.00e+000 7.81e-001f 1
12 2.3676481e+002 8.50e-008 1.67e+000 -1.9 1.06e+004 - 1.00e+000 7.37e-001f 1
13 2.2794093e+002 1.98e-007 1.82e+000 -3.0 6.91e+003 - 9.98e-001 7.00e-001f 1
14 2.2582143e+002 7.63e-008 9.56e-001 -3.2 2.35e+003 - 1.00e+000 7.47e-001f 1
15 2.2529511e+002 2.39e-008 2.72e-001 -4.0 7.00e+002 - 1.00e+000 7.20e-001f 1
16 2.2508076e+002 5.09e-010 2.51e-004 -4.6 2.10e+002 - 1.00e+000 1.00e+000f 1
17 2.2507517e+002 7.65e-011 2.25e-004 -6.7 5.16e+000 - 1.00e+000 8.51e-001f 1
18 2.2507454e+002 1.43e-011 3.79e-005 -6.2 6.63e-001 - 1.00e+000 8.13e-001f 1
19 2.2507438e+002 3.69e-012 1.75e-005 -7.0 1.68e-001 - 1.00e+000 7.43e-001f 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
20 2.2507434e+002 9.33e-013 5.66e-006 -8.2 4.29e-002 - 1.00e+000 7.47e-001f 1
21 2.2507433e+002 2.36e-013 1.64e-006 -8.6 1.09e-002 - 1.00e+000 7.47e-001f 1
22 2.2507432e+002 6.01e-014 1.33e-006 -9.3 2.23e-003 - 1.00e+000 7.45e-001f 1
23 2.2507432e+002 1.42e-014 9.06e-014 -11.0 2.74e-004 - 1.00e+000 1.00e+000h 1
Number of Iterations....: 23
(scaled) (unscaled)
Objective...............: 2.2507432359796402e+002 2.2507432359796402e+002
Dual infeasibility......: 9.0594198809412774e-014 9.0594198809412774e-014
Constraint violation....: 9.4739031434680035e-015 1.4210854715202004e-014
Complementarity.........: 1.2089838737827345e-011 1.2089838737827345e-011
Overall NLP error.......: 1.2089838737827345e-011 1.2089838737827345e-011
Number of objective function evaluations = 24
Number of objective gradient evaluations = 24
Number of equality constraint evaluations = 24
Number of inequality constraint evaluations = 24
Number of equality constraint Jacobian evaluations = 24
Number of inequality constraint Jacobian evaluations = 24
Number of Lagrangian Hessian evaluations = 23
Total CPU secs in IPOPT (w/o function evaluations) = 0.163
Total CPU secs in NLP function evaluations = 0.083
EXIT: Optimal Solution Found.
The solution was found.
The final value of the objective function is 225.07432359796402
---------------------------------------------------
Solver : IPOPT (v3.12)
Solution time : 0.2523 sec
Objective : 225.07433063732404
Successful solution
---------------------------------------------------
我目前正在试用 GEKKO MHE 模式。我在模型中有两个指定的操纵变量和控制变量，以及一个我希望通过 MHE 估计的参数。当我当前 运行 模型时，我得到一个方程定义错误，说
没有等式 (=) 或不等式 (>,<) 的方程式 -267.25544516-267.28925105-267.21324717-267.21191109-264.56454462 正在停止...
模型初始化为：
from gekko import GEKKO
import numpy as np
import matplotlib.pyplot as plt
import pandas as pd
n = 17
m = GEKKO(remote=False)
m.time = np.linspace(0,8,n)
c1_in_arr = np.load('c1_in_arr.npy')
c2_in_arr = np.load('c2_in_arr.npy')
V1_measured = np.load('V1_measured.npy')
V2_measured = np.load('V2_measured.npy')
#mmanipulated variables, feeding in the arrays for them
m.C1_in = m.MV(value=c1_in_arr)
m.C2_in = m.MV(value=c2_in_arr)
#estimated variables, feeding in the upper and lower bounds for them
m.C1_eff = m.FV(value = 0.98, lb = 0.95, ub = 1.0)
#controlled variables, feeding in the measurements for them
m.V1 = m.CV(value=V1_measured)
m.V2 = m.CV(value=V2_measured)
mdot_1 = m.Var()
mdot_2 = m.Var()
m.Equation(mdot_1== 1.52*m.C1_eff*m.C1_in)
m.Equation(mdot_2==-0.668*mdot_1 + 1.33*m.C1_eff*m.C2_in)
df_c = pd.read_csv('Values_C.csv',index_col=0)
Hhat_C1 = m.Var()
Hhat_C1 = m.Var()
M_m = 125
mdot_m = 75
mdot_s = 46
m.Equations([Hhat_C1 == -0.606 + 0.0057 * mdot_1,
Hhat_C2 == -3.933 + 0.00096 * mdot_1])
C1_m = m.Var(value = 200)
C2_m = m.Var(value = 150)
m.Equations([C1_m.dt() == mdot_1 - C1_m/M_m*mdot_m,
C2_m.dt() == mdot_2 - C2_m/M_s*mdot_s)
m.Equation(m.V1==0.8*C1_m/M_m)
m.Equation(m.V2 == 0.78*C1_m/C2_m)
m.options.IMODE = 5
#setting the solver settings to MHE
m.options.EV_TYPE = 1
#setting the solver for the MHE to calculate the parameters based on the sum of absolute errors
m.C1_in.STATUS = 0
m.C2_in.STATUS = 0
m.SiO2_in.STATUS = 0
m.C1_eff.STATUS = 1
m.V1.STATUS = 1
m.V2.STATUS = 1
m.C1_in.FSTATUS = 1
m.C2_in.FSTATUS = 1
m.C1_eff.FSTATUS = 0
m.V1.FSTATUS = 1
m.V2.FSTATUS = 1
m.C1_eff.DMAX = 1.0
m.V1.MEAS_GAP = 0.001
m.V2.MEAS_GAP = 0.001
m.open_folder()
m.solve(disp = False)
当我在求解之前打开 GEKKO 文件夹时，文件夹中也不存在不可行性文件。
当将 MV 和 CV 初始化为“测量”数组的第一个变量时，模型能够 运行 没有错误
例如。 m.C1_in = m.MV(值=c1_in_arr[0])
然而，提供的参数估计不正确。
我认为这个错误可能是由于我的 MV 和 CV 在模型中的处理方式所致。有没有办法查明是哪个方程导致了这个错误，或者是由于 MV/CV 初始化造成的？
谢谢！
在 Gekko 方程中使用 Numpy 数组或 Pandas 数据帧可能会出现问题，例如：
# incorrect
df_c = pd.read_csv('Values_C.csv',index_col=0)
m.Equation(m.C1_in==df_c)
您可以通过创建输入参数来解决此错误，例如：
# correct
df_c = pd.read_csv('Values_C.csv',index_col=0)
df_c = m.Param(df_c)
m.Equation(m.C1_in==df_c)
我没有你的 .npy 文件，所以我无法重现你的错误。但是，我确实用长度为 n 的随机数组输入替换了那些以获得成功的解决方案。还有一些未定义的参数，例如 M_s，因此我包含了一些示例值。您对 MVs 和 CVs 的定义很好。该错误可能是由于其他输入参数在方程中使用之前需要转换为 Gekko 类型参数。
from gekko import GEKKO
import numpy as np
import matplotlib.pyplot as plt
import pandas as pd
n = 17
m = GEKKO(remote=False)
m.time = np.linspace(0,8,n)
c1_in_arr = np.random.rand(n)
c2_in_arr = np.random.rand(n)
V1_measured = np.random.rand(n)
V2_measured = np.random.rand(n)
#mmanipulated variables, feeding in the arrays for them
m.C1_in = m.MV(value=c1_in_arr)
m.C2_in = m.MV(value=c2_in_arr)
#estimated variables, feeding in the upper and lower bounds for them
m.C1_eff = m.FV(value = 0.98, lb = 0.95, ub = 1.0)
#controlled variables, feeding in the measurements for them
m.V1 = m.CV(value=V1_measured)
m.V2 = m.CV(value=V2_measured)
mdot_1 = m.Var()
mdot_2 = m.Var()
m.Equation(mdot_1== 1.52*m.C1_eff*m.C1_in)
m.Equation(mdot_2==-0.668*mdot_1 + 1.33*m.C1_eff*m.C2_in)
Hhat_C1 = m.Var()
Hhat_C2 = m.Var()
M_m = 125
M_s = 125
mdot_m = 75
mdot_s = 46
m.Equations([Hhat_C1 == -0.606 + 0.0057 * mdot_1,
Hhat_C2 == -3.933 + 0.00096 * mdot_1])
C1_m = m.Var(value = 200)
C2_m = m.Var(value = 150)
m.Equations([C1_m.dt() == mdot_1 - C1_m/M_m*mdot_m,
C2_m.dt() == mdot_2 - C2_m/M_s*mdot_s])
m.Equation(m.V1==0.8*C1_m/M_m)
m.Equation(m.V2 == 0.78*C1_m/C2_m)
m.options.IMODE = 5
#setting the solver settings to MHE
m.options.EV_TYPE = 1
#setting the solver for the MHE to calculate the
#parameters based on the sum of absolute errors
m.C1_in.STATUS = 0
m.C2_in.STATUS = 0
m.C1_eff.STATUS = 1
m.V1.STATUS = 1
m.V2.STATUS = 1
m.C1_in.FSTATUS = 1
m.C2_in.FSTATUS = 1
m.C1_eff.FSTATUS = 0
m.V1.FSTATUS = 1
m.V2.FSTATUS = 1
m.C1_eff.DMAX = 1.0
m.V1.MEAS_GAP = 0.001
m.V2.MEAS_GAP = 0.001
m.open_folder()
m.solve(disp = True)
如果存在阻止求解器 运行 的模型错误或存在成功的求解，则不会创建文件 infeasibilities.txt。使用随机输入值，有一个成功的解决方案。
----------------------------------------------------------------
APMonitor, Version 0.9.2
APMonitor Optimization Suite
----------------------------------------------------------------
--------- APM Model Size ------------
Each time step contains
Objects : 0
Constants : 0
Variables : 11
Intermediates: 0
Connections : 0
Equations : 8
Residuals : 8
Warning: CV( 1 ) on at cycle 1 with no MVs on
Warning: CV( 2 ) on at cycle 1 with no MVs on
Number of state variables: 417
Number of total equations: - 416
Number of slack variables: - 0
---------------------------------------
Degrees of freedom : 1
**********************************************
Dynamic Estimation with Interior Point Solver
**********************************************
Info: Exact Hessian
******************************************************************************
This program contains Ipopt, a library for large-scale nonlinear optimization.
Ipopt is released as open source code under the Eclipse Public License (EPL).
For more information visit http://projects.coin-or.org/Ipopt
******************************************************************************
This is Ipopt version 3.10.2, running with linear solver mumps.
Number of nonzeros in equality constraint Jacobian...: 510
Number of nonzeros in inequality constraint Jacobian.: 384
Number of nonzeros in Lagrangian Hessian.............: 32
Total number of variables............................: 417
variables with only lower bounds: 192
variables with lower and upper bounds: 33
variables with only upper bounds: 0
Total number of equality constraints.................: 224
Total number of inequality constraints...............: 192
inequality constraints with only lower bounds: 192
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 1.4079997e+001 1.20e+002 9.00e+000 0.0 0.00e+000 - 0.00e+000 0.00e+000 0
1 2.2358394e+002 1.20e+002 9.95e+000 11.0 1.03e+011 - 1.05e-010 1.45e-012f 1
2 3.0439837e+004 1.20e+002 2.27e+005 12.1 1.14e+012 - 2.78e-013 1.89e-011f 1
3 3.0621616e+006 1.20e+002 2.44e+006 11.4 4.33e+010 - 1.00e+000 4.98e-008f 1
4 3.0621722e+006 6.66e-001 2.49e+004 4.6 3.93e+000 - 9.90e-001 1.00e+000f 1
5 3.0609833e+006 1.78e-014 2.55e+002 2.6 1.28e+000 - 9.90e-001 1.00e+000f 1
6 2.9460876e+006 1.42e-014 2.55e+000 0.6 8.89e+001 - 9.90e-001 1.00e+000f 1
7 7.0161757e+005 2.84e-014 2.55e-002 -1.3 1.69e+003 - 9.90e-001 1.00e+000f 1
8 1.1625511e+004 2.84e-014 2.57e-004 -2.7 1.48e+003 - 9.90e-001 9.91e-001f 1
9 1.0176844e+003 6.17e-009 5.69e-002 -0.1 3.45e+003 - 1.00e+000 9.32e-001f 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
10 4.7702371e+002 1.77e-008 3.10e+000 -0.8 8.48e+003 - 1.00e+000 6.38e-001f 1
11 2.8271410e+002 2.82e-007 1.44e+000 -1.0 5.55e+003 - 1.00e+000 7.81e-001f 1
12 2.3676481e+002 8.50e-008 1.67e+000 -1.9 1.06e+004 - 1.00e+000 7.37e-001f 1
13 2.2794093e+002 1.98e-007 1.82e+000 -3.0 6.91e+003 - 9.98e-001 7.00e-001f 1
14 2.2582143e+002 7.63e-008 9.56e-001 -3.2 2.35e+003 - 1.00e+000 7.47e-001f 1
15 2.2529511e+002 2.39e-008 2.72e-001 -4.0 7.00e+002 - 1.00e+000 7.20e-001f 1
16 2.2508076e+002 5.09e-010 2.51e-004 -4.6 2.10e+002 - 1.00e+000 1.00e+000f 1
17 2.2507517e+002 7.65e-011 2.25e-004 -6.7 5.16e+000 - 1.00e+000 8.51e-001f 1
18 2.2507454e+002 1.43e-011 3.79e-005 -6.2 6.63e-001 - 1.00e+000 8.13e-001f 1
19 2.2507438e+002 3.69e-012 1.75e-005 -7.0 1.68e-001 - 1.00e+000 7.43e-001f 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
20 2.2507434e+002 9.33e-013 5.66e-006 -8.2 4.29e-002 - 1.00e+000 7.47e-001f 1
21 2.2507433e+002 2.36e-013 1.64e-006 -8.6 1.09e-002 - 1.00e+000 7.47e-001f 1
22 2.2507432e+002 6.01e-014 1.33e-006 -9.3 2.23e-003 - 1.00e+000 7.45e-001f 1
23 2.2507432e+002 1.42e-014 9.06e-014 -11.0 2.74e-004 - 1.00e+000 1.00e+000h 1
Number of Iterations....: 23
(scaled) (unscaled)
Objective...............: 2.2507432359796402e+002 2.2507432359796402e+002
Dual infeasibility......: 9.0594198809412774e-014 9.0594198809412774e-014
Constraint violation....: 9.4739031434680035e-015 1.4210854715202004e-014
Complementarity.........: 1.2089838737827345e-011 1.2089838737827345e-011
Overall NLP error.......: 1.2089838737827345e-011 1.2089838737827345e-011
Number of objective function evaluations = 24
Number of objective gradient evaluations = 24
Number of equality constraint evaluations = 24
Number of inequality constraint evaluations = 24
Number of equality constraint Jacobian evaluations = 24
Number of inequality constraint Jacobian evaluations = 24
Number of Lagrangian Hessian evaluations = 23
Total CPU secs in IPOPT (w/o function evaluations) = 0.163
Total CPU secs in NLP function evaluations = 0.083
EXIT: Optimal Solution Found.
The solution was found.
The final value of the objective function is 225.07432359796402
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Solver : IPOPT (v3.12)
Solution time : 0.2523 sec
Objective : 225.07433063732404
Successful solution
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