Try our new documentation site (beta).


bilinear.py


#!/usr/bin/env python3.7

# Copyright 2021, Gurobi Optimization, LLC

# This example formulates and solves the following simple bilinear model:
#  maximize    x
#  subject to  x + y + z <= 10
#              x * y <= 2         (bilinear inequality)
#              x * z + y * z = 1  (bilinear equality)
#              x, y, z non-negative (x integral in second version)

import gurobipy as gp
from gurobipy import GRB

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

# Create variables
x = m.addVar(name="x")
y = m.addVar(name="y")
z = m.addVar(name="z")

# Set objective: maximize x
m.setObjective(1.0*x, GRB.MAXIMIZE)

# Add linear constraint: x + y + z <= 10
m.addConstr(x + y + z <= 10, "c0")

# Add bilinear inequality constraint: x * y <= 2
m.addConstr(x*y <= 2, "bilinear0")

# Add bilinear equality constraint: x * z + y * z == 1
m.addConstr(x*z + y*z == 1, "bilinear1")

# First optimize() call will fail - need to set NonConvex to 2
try:
    m.optimize()
except gp.GurobiError:
    print("Optimize failed due to non-convexity")

# Solve bilinear model
m.params.NonConvex = 2
m.optimize()

m.printAttr('x')

# Constrain 'x' to be integral and solve again
x.vType = GRB.INTEGER
m.optimize()

m.printAttr('x')

Try Gurobi for Free

Choose the evaluation license that fits you best, and start working with our Expert Team for technical guidance and support.

Evaluation License
Get a free, full-featured license of the Gurobi Optimizer to experience the performance, support, benchmarking and tuning services we provide as part of our product offering.
Academic License
Gurobi supports the teaching and use of optimization within academic institutions. We offer free, full-featured copies of Gurobi for use in class, and for research.
Cloud Trial

Request free trial hours, so you can see how quickly and easily a model can be solved on the cloud.

Search

Gurobi Optimization