Maximizing convex function

Answered

Hussein Sharadga

November 24, 2022 04:39 Edited

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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

• Nonconvex

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  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.

  Best regards, 
  Jaromił

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  Hussein Sharadga

  November 24, 2022 18:50 Edited

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  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

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  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

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