Quadratic equality constraints are non-convex

Answered

Lorenzo Steccanella

July 21, 2021 14:27

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Hi all,

I formulate the following problem in Gurobi:

that I belive should be convex but I get the error "GurobiError: Quadratic equality constraints are non-convex".

Can anyone tell me how to check in Gurobi why this formulation is Non-Convex? ... there is a way to convert this in a convex problem?

Here, you can find the code to reproduce the error:

import gurobipy as gp
from gurobipy import GRB

model = gp.Model("quad")

d = 2
x1 = model.addVars(d, name="x1", lb=-GRB.INFINITY, ub=+GRB.INFINITY)
x2 = model.addVars(d, name="x2", lb=-GRB.INFINITY, ub=+GRB.INFINITY)
x3 = model.addVars(d, name="x3", lb=-GRB.INFINITY, ub=+GRB.INFINITY)
Y = model.addVars(2, name="y", lb=-GRB.INFINITY, ub=+GRB.INFINITY)

### OBJECTIVE ###
obj = Y[0] + Y[1]
model.setObjective(obj, GRB.MINIMIZE)

### CONSTRAINS ###
model.addConstr(Y[0] >= 0)
model.addConstr(Y[1] >= 0)
model.addConstr(Y[0] + ((x1[0] - x2[0])**2 + (x1[1] - x2[1])**2) - 1 == 0)
model.addConstr(Y[1] + ((x2[0] - x3[0])**2 + (x2[1] - x3[1])**2) - 1 == 0)

model.optimize()

 

Thanks!

 

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• Official comment

  

  Simranjit Kaur

  • Gurobi Staff

  June 23, 2025 02:51 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?.
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  Mario Ruthmair

  • Gurobi Staff

  July 23, 2021 11:40 Edited

  Hi Lorenzo,

  quadratic equality constraints are never convex. The feasible set usually contains discrete points that are not connected and thus the set is non-convex.

  Best regards,
  Mario

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