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Logarithmic Optimization Problem

Answered
XIAO ROU YU
Edited
  • Gurobi-versary
  • First Comment
  • First Question

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!!!
 

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Comments

6 comments

Date Votes
  • Official comment
    Simranjit Kaur
    • Gurobi Staff
    This post is more than two years old. Some information may not be up to date. For current information, please check the Gurobi Documentation or Knowledge Base. If you need more help, please create a new post in the community forum, or try Gurobot, our chatbot interface offering instant, expert-level support.
  • David Torres Sanchez
    • Gurobi Staff
    Edited

    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

    0
  • XIAO ROU YU
    Edited
    • Gurobi-versary
    • First Comment
    • First Question

    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!
    0
  • David Torres Sanchez
    • Gurobi Staff

    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

    0
  • XIAO ROU YU
    • Gurobi-versary
    • First Comment
    • First Question

    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?

    0
  • David Torres Sanchez
    • Gurobi Staff

    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

    0

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