Why Gurobi cannot find the solution to a simple Quadratic Optimization Problem?

Answered

Zhongjin Lu

September 11, 2024 01:01

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import gurobipy as gp
from gurobipy import GRB
import numpy as np
import scipy.sparse as sp

# Create a new model
m = gp.Model("matrix1")

# Create variables
x = m.addMVar(shape=7, vtype=GRB.CONTINUOUS, name="x")
# Set objective
obj = np.array([1, -0.1, 0.8, 0.3, 0.9,0.4,0.4])*0.01 # expected monthly returns
m.setObjective(obj @ x , GRB.MAXIMIZE) #50bps per trade; 50bps per month for shorting

Sigma_psd = np.diag(np.array([30, 0.2, 20, 16, 32, 28, 19])*0.0001)
# Define the quadratic constraint; 5% per month for the portfolio
V = (0.05) ** 2

# Add the quadratic constraint to the model
m.addConstr(x @ Sigma_psd @ x == V, name="quadratic_constraint")


# Optimize model
m.optimize()
weights = x.X
print("Weights from Gurobi:", ", ".join(f"{w:g}" for w in weights))
print(f"Obj: {m.ObjVal:g}")


Sigma_inv = np.linalg.inv(Sigma_psd)  # Inverse of Sigma
weights = np.dot(Sigma_inv, obj)   # Dot product of inv(Sigma) and obj
weights = np.sqrt(V/np.dot(weights.T, np.dot(Sigma_psd, weights)))*weights
print("Correct Weights:", ", ".join(f"{w:g}" for w in weights))
print(f"Obj under Correct Weights: {np.dot(weights.T, obj):g}")
 

Related to

• QCP

0

• Official comment

  

  Simranjit Kaur

  • Gurobi Staff

  November 13, 2026 01:20

  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.
• 

  Ahmed Azab

  • Gurobi Staff

  September 11, 2024 02:01 Edited

  Hi,
  I solved your model using Gurobi version 11.0.3. 

  Optimal solution found (tolerance 1.00e-04)
  Best objective 1.661528493733e-02, best bound 1.661528493733e-02, gap 0.0000%

  Note that the default lower bound value for the variables is 0.
  
  Regards
  -Ahmed
  
  
  

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  Zhongjin Lu

  September 11, 2024 15:07

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  Ahmed,

  Thanks a lot. I didn't realize that the default lower bound value is 0. Once I relax it, Gurobi finds the correct answer. Thanks!

  Zhongjin

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