How can I linearize a quadratic equation or constraint?

Answered

Laura Morejon Ramirez

• April 12, 2022 22:17
• Edited

I have a multi-objective optimization problem, of which the first equation includes a quadratic element. It is my understanding that quadratic equations cannot be handled in multi-objective problems, and that they often increase solving time. So, I want to linearize it to make it easy. The part of my objective function that includes a quadratic element is:

obj_profit += gp.quicksum(N_f[key[0], key[2]] * N_P[key] * b for key in routing_key)

Where \( N_{P,r} \) and  \( N_{F,m} \) are optimization variables in the form of positive integers subject to certain constraints. In order to linearize the problem, I have added the constraint:

gurobi_model.addConstrs((N_P[key] * N_F[key[0], key[2]] == N_freq_times_p[key] for key in routing_key), "Freq_Premium_Times_Pax")

so that the objective function now becomes: 

obj_profit += gp.quicksum(N_freq_times_p[key] * b for key in routing_key)

However, I still get the error message gurobipy.GurobiError: Quadratic equality constraints are non-convex. Set NonConvex parameter to 2 to solve model.

Is there a step I am missing in the linearization of the equation?

 

Thanks in advance!

 

0

• 

  Maliheh Aramon

  Gurobi Staff

  • April 13, 2022 02:56

  Hi Laura,

  The added equality quadratic constraints makes the problem nonconvex and you need to explicitly set the parameter NonConvex=2 to tell Gurobi that it needs to solve a nonconvex problem. 

  Best regards,

  Maliheh 

  0

Please sign in to leave a comment.