How to linearize the nonlinear constraint in modelling

Answered

Cass C

December 10, 2021 18:57

• 
• 
• 

hi gurobi teams:

I am trying to use PWL method on tackling my nonlinear constraints, e.g., z^2=x^2-y^2

I have went through an example on the gurobi portal and found this:

import gurobipy as gp
from math import exp

def f(u): 
  return exp(-u)

def g(u): 
  return 2 * u * u - 4 * u

try: 
  # Create a new model 
  m = gp.Model()
  # Create variables 
  lb = 0.0 
  ub = 1.0 
  x = m.addVar(lb, ub, name='x') 
  y = m.addVar(lb, ub, name='y') 
  z = m.addVar(lb, ub, name='z') 
  # Set objective for y 
  m.setObjective(-y) 
  # Add piecewise-linear objective functions for x and z 
  npts = 101 
  ptu = [] 
  ptf = [] 
  ptg = [] 
  for i in range(npts): 
    ptu.append(lb + (ub - lb) * i / (npts - 1)) 
    ptf.append(f(ptu[i])) 
    ptg.append(g(ptu[i]))

m.setPWLObj(x, ptu, ptf) 
m.setPWLObj(z, ptu, ptg) 
# Add constraint: x + 2 y + 3 z <= 4 
m.addConstr(x + 2 * y + 3 * z <= 4, 'c0') 
# Add constraint: x + y >= 1 
m.addConstr(x + y >= 1, 'c1') 
# Optimize model as an LP 
m.optimize

It seems like the nonlinear term in objective function is linearized, but what should I do if I want linearize the nonlinear in constraints? 

many thanks! 

0

• Official comment

  

  Simranjit Kaur

  • Gurobi Staff

  June 23, 2025 02:43 Edited

  This post is more than three 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 why not try our AI Gurobot?.
• 

  Jaromił Najman

  • Gurobi Staff

  December 13, 2021 10:46 Edited

  Hi,

  Could you please elaborate why you have to linearize the nonlinear terms on your own?

  Gurobi can solve non-convex quadratically constrained problem meaning that you can introduce the term \(z^2 = x^2 - y^2\) as a constraint via

  m.addConstr(z*z == x*x - y*y, name="myConstr")

  For terms such as \(\exp\) or \(\log\), you can use the general constraint methods.

  Best regards, 
  Jaromił

  0
• 

  Cass C

  January 01, 2022 09:46

  • 
  • 
  • 

  Hi Jaromił

  Thanks for you replying. If I try NLP in my model, it will be tough to solve as there are a large amount of variables. So that is why I have to linearise it. I tried SOCP before and it was fast but the accuracy is not good, so I am going to use PWL.

  Many thanks!

   

   

  0

Post is closed for comments.