hyperbolic sine of the elements of X

Answered

Abde

• May 19, 2023 13:25
• Edited

Hi,

Does Gurobi Python, has sinh(x), which stands for hyperbolic sine of the elements of X.

I utilized Model.addGenConstrSin, but when I searched on the internet I found that this attribute is different from sinh(x) that I am looking to implement, and therefore, the result is not good.

Could you please let me know if gurobi has an attribute regarding this.

Thank you in advance,

 

#calculating the size of the uncertainty set under the assumption that the uncertainty is
#bounded and symmetric which is satisfied in this example
#parameters
eps=0.5
mu=0.1 #abs(E(r.v)= 0.1)
j=1
#Set of Constraints
m.addGenConstrSin(theta,x)
m.addGenConstrCos(theta,y)
m.addConstr(t == x+y)
m.addGenConstrLog(t,f)
m.addConstr(-theta*delta_gmf + j*f <= math.log(eps))
Z=delta_gmf
m.setObjective(Z, GRB.MINIMIZE)
m.params.NonConvex = 2
m.optimize()

Related to

• Nonlinear
• General Constraints

1

• 

  Maliheh Aramon

  Gurobi Staff

  • May 20, 2023 02:48

  Hi, 

  The hyperbolic sine function equals \(\sinh(x) = \frac{e^{x} - e^{-x}}{2}\). You can use the method Model.addGenConstrExp() to model the natural exponential function. See the example script below:

  import gurobipy as gp
  from gurobipy import GRB
  
  m = gp.Model()
  sinh = m.addVar(lb=-GRB.INFINITY, name="sinh")
  # It is important to set the lb and ub of the x and x_minus variables 
  # to the tightest possible values depending on your application
  x = m.addVar(lb=-GRB.INFINITY, name="x")
  x_minus = m.addVar(lb=-GRB.INFINITY, name="x_minus")
  y = m.addVar(name="y")
  y_minus = m.addVar(name="y_minus")
  
  # Define y = exp(x)
  m.addGenConstrExp(x, y)
  # Define y_minus = exp(x_minus) = exp(-x)
  m.addGenConstrExp(x_minus, y_minus)
  # Define the relationship between x and x_minus
  m.addConstr(x == -1*x_minus)
  # Define hyperbolic sine function
  m.addConstr(sinh == 0.5 * (y - y_minus))

  Best regards,

  Maliheh

  1
• 

  Abde

  • May 20, 2023 17:39

  

  

  

  Hello Ms. Maliheh,

  Thank you so much for your feedback, it is really helpful.

  I have just noticed that a mistake has been made on your shared code;

  which I think should be like the following; (please correct me if I am wrong).

  # Define the relationship between x and x_minus
  m.addConstr(x_minus == -1*x)

  Best Regard,

  0
• 

  Maliheh Aramon

  Gurobi Staff

  • May 23, 2023 19:55

  Hi, 

  If you multiply both sides of the constraint \(x_{\text{minus}} = - x\) by -1, we get the constraint \(-x_{\text{minus}} = x\). Therefore, your version is mathematically equivalent to the constraint implemented in our script. 

  Best regards,

  Maliheh

  0

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