我希望在使用Python Gekko时，在优化过程的每一次迭代中获得变量的值.
例如，文档(https://gekko.readthedocs.io/en/latest/quick_start.html#example)中的以下代码解决了问题HS71:
from gekko import GEKKO
import numpy as np
m = GEKKO(remote=False)
x = m.Array(m.Var, 4, value=1, lb=1, ub=5)
x1, x2, x3, x4 = x # rename variables
x2.value = 5; x3.value = 5 # change guess
m.Equation(np.prod(x) >= 25) # prod>=25
m.Equation(m.sum([xi**2 for xi in x]) == 40) # sum=40
m.Minimize(x1*x4*(x1 + x2 + x3) + x3) # objective
m.solve()
print(x, m.options.OBJFCNVAL)
控制台中显示的输出如下:
----------------------------------------------------------------
APMonitor, Version 1.0.0
APMonitor Optimization Suite
----------------------------------------------------------------
--------- APM Model Size ------------
Each time step contains
Objects : 1
Constants : 0
Variables : 10
Intermediates: 0
Connections : 5
Equations : 7
Residuals : 7
Number of state variables: 10
Number of total equations: - 7
Number of slack variables: - 1
---------------------------------------
Degrees of freedom : 2
**********************************************
Steady State Optimization 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...: 19
Number of nonzeros in inequality constraint Jacobian.: 0
Number of nonzeros in Lagrangian Hessian.............: 10
Total number of variables............................: 10
variables with only lower bounds: 1
variables with lower and upper bounds: 4
variables with only upper bounds: 0
Total number of equality constraints.................: 7
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 1.6109693e+001 4.00e+001 5.24e-001 0.0 0.00e+000 - 0.00e+000 0.00e+000 0
1 1.6896037e+001 7.28e-001 7.82e-001 -0.9 4.00e+001 - 1.00e+000 1.00e+000h 1
2 1.7121828e+001 1.66e-001 6.51e-001 -1.1 2.15e+000 - 8.23e-001 1.00e+000h 1
3 1.6954231e+001 1.60e-001 6.46e-002 -2.1 6.34e-001 - 1.00e+000 1.00e+000h 1
4 1.7008327e+001 1.68e-002 1.22e-002 -2.9 3.39e-001 - 9.94e-001 1.00e+000h 1
5 1.7013921e+001 3.15e-004 1.47e-004 -4.6 3.56e-002 - 1.00e+000 1.00e+000h 1
6 1.7014017e+001 2.51e-007 4.50e-007 -10.5 5.56e-004 - 9.99e-001 1.00e+000h 1
Number of Iterations....: 6
(scaled) (unscaled)
Objective...............: 1.7014017181012623e+001 1.7014017181012623e+001
Dual infeasibility......: 4.5045555432827566e-007 4.5045555432827566e-007
Constraint violation....: 2.5086595754315365e-007 2.5086595754315365e-007
Complementarity.........: 4.8294565936715572e-008 4.8294565936715572e-008
Overall NLP error.......: 4.5045555432827566e-007 4.5045555432827566e-007
Number of objective function evaluations = 7
Number of objective gradient evaluations = 7
Number of equality constraint evaluations = 7
Number of inequality constraint evaluations = 0
Number of equality constraint Jacobian evaluations = 7
Number of inequality constraint Jacobian evaluations = 0
Number of Lagrangian Hessian evaluations = 6
Total CPU secs in IPOPT (w/o function evaluations) = 0.014
Total CPU secs in NLP function evaluations = 0.000
EXIT: Optimal Solution Found.
The solution was found.
The final value of the objective function is 17.014017181012623
---------------------------------------------------
Solver : IPOPT (v3.12)
Solution time : 0.021100000000000008 sec
Objective : 17.014017181012623
Successful solution
---------------------------------------------------
[[1.0000000339] [4.7429996271] [3.8211500196] [1.3794082228]] 17.014017181
这包括目标函数在每次迭代时的值，但我还希望在每次迭代时获得变量(x)的值.