Cannot set objective function. minimize max(var.values())

Answered

Matt Hall

January 25, 2022 06:13 Edited

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I have an objective I am trying to cast as follows. 

m.setObjective(max(X.values(), sense=GRB.MINIMIZE))

But I am getting a type error. 

TypeError: '>' not supported between instances of 'Var' and 'Var'

My derived variable, X, is defined as follows.

X = m.addVars(range(len(n)), vtype=GRB.CONTINUOUS, lb=0, ub=100, name="X")

The rest of my model is somewhat complex. X depends on a sum of smaller values, and these smaller values depend on two binary decision variables. I'm curious if my problem is more surface level though. Please let me know if you see anything clearly wrong with these definitions, or if you need more detail about constraints relating to X. 

For what it is worth, I do not have any strict less-than comparisons in any of my constraints.

Thank you. 

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• Official comment

  

  Simranjit Kaur

  • Gurobi Staff

  November 16, 2025 23:45

  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 try Gurobot, our chatbot interface offering instant, expert-level support.
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  Jonasz Staszek

  • Community Moderator

  January 25, 2022 13:46

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  It seems to me that you would need to reformulate your model somehow. Perhaps this other thread will be of help.

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  Jaromił Najman

  • Gurobi Staff

  January 26, 2022 08:54

  Jonasz is right. If you want to use Gurobi's max_ function, you have to introduce an auxiliary variable and an equality constraint to model it, e.g.,

  import gurobipy as gp
  from gurobipy import GRB
  
  m = gp.Model("test")
  x = m.addVars(5, vtype=GRB.CONTINUOUS, lb=0, ub=100, name="X")
  z = m.addVar(vtype=GRB.CONTINUOUS, name="Z")
  # Add constraint z = max(x1,x2,x3,x4,x5)
  m.addConstr(z == gp.max_(x), name="max_contraint")
  m.setObjective(z, sense=GRB.MINIMIZE)

  Best regards,
  Jaromił

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