Maximizing convex function

Answered

Hussein Sharadga

• November 24, 2022 04:39
• Edited

Hi!

I believe convex optimization means to find the minimum of a convex function or the maximum of a concave function ( maximum of a concave function == minimum of -concave function, -concave function==convex function).

I tried to find the maximum of a convex function, and it solved it. Does that mean gurobipy replaces the objective function with a piecewise linear function? 

 

#
import gurobipy as gp
from gurobipy import GRB
m=gp.Model()
x=m.addVar(vtype='C',lb=0,ub=1)
m.setObjective(x**2-0.6*x, GRB.MAXIMIZE)
m.optimize()

 

Related to

• Python
• Nonconvex

1

• 

  Jaromił Najman

  Gurobi Staff

  • November 24, 2022 10:57

  Hi,

  Does that mean gurobipy replaces the objective function with a piecewise linear function? 

  No, Gurobi only uses piecewise-linear approximations if you use the addGenConstr methods.

  For nonconvex models, Gurobi uses the spatial B&B approach.

  In your particular case, the model is so easy, that Gurobi is able to solve it in its presolve step. Note that usually (if the model is not so simple), you have to set the parameter NonConvex=2 in order to solve nonconvex models.

  Best regards, 
  Jaromił

  1
• 

  Hussein Sharadga

  • November 24, 2022 18:50
  • Edited

  

  

  

  Thank you so much! Jaromił Najman 

  I am working on a large-scale problem and wanted to know if all constraints are linear or convex with a nonconvex objective function that gurobipy can solve it in affordable computing time.

   

  Best,

  Hussein

  0
• 

  Jaromił Najman

  Gurobi Staff

  • November 25, 2022 08:22

  Hi Hussein,

  I am working on a large-scale problem and wanted to know if all constraints are linear or convex with a nonconvex objective function that gurobipy can solve it in affordable computing time.

  This cannot be stated a priori. The only way to find out is to actually construct the model and try to solve it.

  Best regards, 
  Jaromił

  1

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