IPOPT消息和Gekko消息的区别

Question

Good morning, I'm currently using Gekko in dynamic optimization. The simulation I've run indicates that it´s converging.

from gekko import GEKKO
m = GEKKO()
x = m.Array(m.Var,3)
m.Equation(3*x[0]-2*x[1]**2==7)
m.Equation(4*x[0]-x[2]**2==11)
m.Equation(3*x[0]-2*x[1]**2-7==(3*x[0]-2*x[1]**2-7)**2)
m.Minimize(4*x[0]**2 + 2*x[1]**2 + 2*x[2]**2\
           -33*x[0]  + 16*x[1]  - 24*x[2])
m.solve()

Number of objective function evaluations             = 62
Number of objective gradient evaluations             = 10
Number of equality constraint evaluations            = 63
Number of inequality constraint evaluations          = 0
Number of equality constraint Jacobian evaluations   = 30
Number of inequality constraint Jacobian evaluations = 0
Number of Lagrangian Hessian evaluations             = 28
Total CPU secs in IPOPT (w/o function evaluations)   =      0.024
Total CPU secs in NLP function evaluations           =      0.002

EXIT: Optimal Solution Found.

 The solution was found.

 The final value of the objective function is    343.408879673171     

 ---------------------------------------------------
 Solver         :  IPOPT (v3.12)
 Solution time  :   4.040000001259614E-002 sec
 Objective      :    343.408879673171     
 Successful solution
 ---------------------------------------------------

However, when I review the results of the IPOPT details it indicates the following error.

  27r 3.4340888e+02 1.20e-06 3.85e-01  -9.0 5.66e-06   1.8 1.00e+00 8.54e-01f  1
  28r 3.4340888e+02 1.20e-08 5.23e-03  -9.0 1.20e-06   1.3 1.00e+00 9.86e-01h  1
Cannot recompute multipliers for feasibility problem.  Error in eq_mult_calculator

How can I interpret this error? Thank you very much for your attention.

Answer 1

From IPOPT issue tracking #69 :

There is now a new return code (FOUND_FEASIBLE_POINT and Found_Feasible_Point) that is returned when Ipopt found a feasible for a square problem, but the multipliers might be off.

The problem is with equation 3 that is a degenerate equation and makes it so the Lagrange multiplier calculation may be wrong:

m.Equation(3*x[0]-2*x[1]**2-7==(3*x[0]-2*x[1]**2-7)**2)

It is degenerate because m.Equation(3*x[0]-2*x[1]**2==7) is also included. Equation 3 is not needed to solve the problem. Your problem may also have a degenerate equation but the solution is still valid.