Logarithmic Optimization Problem

回答済み

XIAO ROU YU

2024年05月09日 13:19 編集済み

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I am very new in using Gurobi, and I encounter some problem when using "addGenConstrLog".

I try to solve a complicated log-optimal problem, and I first tried a simple version

where w is an unit simplex and X is daily history return.

 

Below is my code:

import numpy as np
import gurobipy as gp
from gurobipy import GRB

model = gp.Model()

N=2
n=2

w = model.addMVar((n, 1), name="w")

w_t = w.transpose()
R_h = np.array(R_hat)
# R_h=np.array[[ 4.00959308e-03 -1.35401866e-04] [ 7.39726027e-05 7.39726027e-05]]

model.addConstrs((w[i] >= 0 for i in range(n)), name="w_nonnegativity")
model.addConstr(w.sum() == 1, name="w_sum_to_1")

x1 = model.addVar(name="x1")
x2 = model.addVar(name="x2")
y1 = model.addVar(name="y1")
y2 = model.addVar(name="y2")

model.addConstr(x1 == 1 + w_t @ R_h[:, 0])
model.addConstr(y1 == 1 + w_t @ R_h[:, 1])
model.addGenConstrLog(x1, x2, name="log_term1")
model.addGenConstrLog(y1, y2, name="log_term1")

objective = (1/N) * (x2+y2)

model.setObjective(objective, sense=GRB.MAXIMIZE)

model.Params.FuncPieces = 100 
model.params.FuncPieceError = 1e-6 

model.optimize() 

print(f'optimal value w: {w.X}')

 

Problem:

After running this code, I got an optimal value 7.316836268101e-04, and optimal solution w: [[0.35330288] [0.64669712]]

But it is obvious that the optimal solution is w:[[1] [0]] and I also use this solution to calculate an optimal value = 0.001933081779322477

 

I don't know why I got this answer?

I think my code is correct.

Thanks for answering!!!

 

関連

• Python

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  David Torres Sanchez

  • Gurobi Staff

  2024年05月09日 13:25 編集済み

  Hi Xiao,

  Can you try using the latest version (v11.0.1) and setting the parameter FuncNonlinear=1 (instead of the ones you are setting)

  Cheers, 
  David

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  XIAO ROU YU

  2024年05月09日 15:07 編集済み

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  Hi David,

  I already use the latest version(v11.0.1) and setting the parameter

  model.Params.FuncNonlinear=1

  But still got the same results...

   

  I wonder if my origin code is wrong?

   

  Here's my output:

  

   

  I noticed that there are gap 0.0011%

   

  Thank you!

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  David Torres Sanchez

  • Gurobi Staff

  2024年05月09日 17:17

  Hi Xiao,

  Thanks for the extra output. When creating variables the default lower bound is 0.
  Hence that solution is not allowed, if we allow the \(\texttt{y}\) variable to be negative:

  y1 = model.addVar(name="y1", lb=-1000)
  y2 = model.addVar(name="y1", lb=-1000) # Only this one is needed

  We get (roughly) the expected result:

  Best objective 1.933075925509e-03, best bound 1.933093487611e-03, gap 0.0009%
  optimal value w: [[9.99996442e-01], [3.55767355e-06]]

  Cheers, 
  David

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  XIAO ROU YU

  2024年05月09日 20:04

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  Hi David,

  Thanks a lot !

  "When creating variables the default lower bound is 0."

  This is very helpful for me.

  But I still want to ask why there are nonzero gap?

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  David Torres Sanchez

  • Gurobi Staff

  2024年05月10日 08:58

  Hi Xiao,

  This is lower than the default MIPGap (1e-4).

  You are right, setting the MIPGap explicitly to 0 we get:

  Best objective 1.933093486649e-03, best bound 1.933093486649e-03, gap 0.0000%
  optimal value w: [[1.], [0.]]

  Cheers, 
  David

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