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bilinear.py
#!/usr/bin/env python3.7
# Copyright 2023, 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')
