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Using sqrt in constraint.

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  • Ronald van der Velden
    Gurobi Staff Gurobi Staff

    Hi,

    Because of your question and you mentioning "risk", I suspect you may be interested in the Gurobi Finance project. The linked page includes a nice and clean way to express this risk formula using Gurobi matrix notation. The project contains many more articles showing how to express related concepts with Gurobi.

    Now specifically about sqrt :

    • If you include risk as an objective, you may not need to apply sqrt at all
    • If you add a constraint to limit risk, you would take the square of the right-hand side (constant) to avoid having to take sqrt of the left-hand-side (formula involving your decision variables)

    Let me know if this helps!

    Kind regards,
    Ronald

    1
  • Jai Kishan Gupta
    First Question
    Conversationalist

    my constraint is result = np.sqrt(np.dot(np.dot(variable_array.T,covariance_matrix_array),variable_array))

    where result should be less than 5.56%. Now to remove the sqrt from left hand side if I square the 0.056 then the answer will not be right.

    0
  • Ronald van der Velden
    Gurobi Staff Gurobi Staff

    What is the problem you're observing? 

    0
  • Jai Kishan Gupta
    First Question
    Conversationalist

    I am creating a constraint the contraint is risk should be less that 5.56% to caluclate the risk we have formula risk = np.sqrt(np.dot(np.dot(variable_array.T,covariance_matrix_array),variable_array)). Now that gurobi does not support sqrt so how can I create the constraint?

    0
  • Ronald van der Velden
    Gurobi Staff Gurobi Staff

    Hi,

    What I meant was - have you implemented the approach I suggested and/or tested the model that is discussed in Gurobi Finance? If that leads to errors, could you share a reproducible piece of code to better understand what you're trying to do?

    If risk = sqrt(f(vars)) and your only constraint on risk is risk<=0.056, then defining riskSquared=f(vars) and riskSquared<=0.056**2 should give the right result.

    Just for completeness - Gurobi does support the square root, using the addGenConstrPow function. You would first define a variable riskSquared as above, and then another variable risk which you would link by calling addGenConstrPow(riskSquared, risk, 0.5). For performance reasons however you should prefer the approach I shared earlier.

    Kind regards,
    Ronald

    0
  • Jai Kishan Gupta
    First Question
    Conversationalist

    I have implemented the solution now the error is not coming but a new problem arrives here is the code 

    portfolio_risk = gp.QuadExpr()
    for i in range(len(variable)):
        for j in range(len(variable)):
            portfolio_risk += variable[i] * covariance_matrix_array[i, j] * variable[j]
    model.addQConstr(portfolio_risk <= 0.00287296, "portfolio_risk")
    model.update()

    The output is 

    <gurobi.QConstr Not Yet Added>

    Why the constraint is not get added when I also tried to update the model after adding the constraint

    0
  • Ronald van der Velden
    Gurobi Staff Gurobi Staff

    Does the error occur at the last line of your code (model.update) or in a different place? It would typically occur when you try referencing a constraint later, but I notice you don't store the result of model.addQConstr in a Python variable for use later.

    Kind regards,
    Ronald

    0
  • Jai Kishan Gupta
    First Question
    Conversationalist

    It's not get added even after doing model.update()

    see the code 

    portfolio_risk = gp.QuadExpr()
    for i in range(len(variable)):
        for j in range(len(variable)):
            portfolio_risk += variable[i] * covariance_matrix_array[i, j] * variable[j] 
    model.addQConstr(portfolio_risk <= 0.00287296, "portfolio_risk")

    Output:

    <gurobi.QConstr Not Yet Added>

    The solution provided by you

    model.update()

    Checking for the constraint in the model

    pending_constraints = model.getConstrs()

    # Print details of each pending constraint
    for constr in pending_constraints:
        print(constr)

    No output None
    Additional info:
    This is how my portflolio_risk look like 

    <gurobi.QuadExpr: 0.0 + [ 8.430925170068025e-05 x1 ^ 2 + 0.000510914923469388 x2 * x1 + -0.00022443623724489845 x3 * x1 + -0.0003129861011904759 x4 * x1 + 0.0003389425255102042 x5 * x1 + -0.0001981796896258504 x6 * x1 + 0.0006025277593537417 x7 * x1 + -0.0002102003188775508 x8 * x1 + 0.0005607082695578237 x9 * x1 + 0.00013936514455782303 x10 * x1 + 0.0003629431972789119 x11 * x1 + 0.00041692561649659884 x12 * x1 + 0.00036367504251700705 x13 * x1 + 2.4184438775510693e-06 x14 * x1 + 0.0011259449319727898 x15 * x1]
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  • Jai Kishan Gupta
    First Question
    Conversationalist

    The problem is solve 

    pending_constraints = model.getConstrs()

    I have using getConstrs() for getting 

    addQConstr

    I have used model.getQConstrs() now it's showing Thank Your for the help sir.

    0

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