Fraction with quadratic numerator as objective function

回答済み

Tobias Tillipaul

2022年12月23日 19:44

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Hi all,

I am currently trying to implement the following expression as objective function to my model (a, b being vectors of constant values):

I found out that I could construct the first part of the numerator as GRBQuadExpr, but subsequently I figured I could just express the second part of the numerator and the denominator as GRBLinExpr and add the pieces together - and failed to do so. Moreover, there is no "/" operator defined for GRBQuadExpr and GRBLinExpr, thus I am wondering if Gurobi has the means to construct such an expression and add them to models. Is there a predefined way to create fractional expressions or a common workaround that allows to use this expression or an abstraction of it?

Thanks in advance for any help, enjoy the holidays.

Best regards,

Tobias Tillipaul

関連

• Formulation
• MINLP

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• 正式なコメント

  

  Simranjit Kaur

  • Gurobi Staff

  2026年11月13日 01:51

  This post is more than two years old. Some information may not be up to date. For current information, please check the Gurobi Documentation or Knowledge Base. If you need more help, please create a new post in the community forum, or try Gurobot, our chatbot interface offering instant, expert-level support.
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  Maliheh Aramon

  • Gurobi Staff

  2022年12月24日 03:09

  Hi Tobias, 

  To model a fractional expression like \(\frac{x}{y}\) with \(x\) and \(y\) being quadratic and linear expression, respectively, you need to define an auxiliary variable \(z\) where \(z = \frac{x}{y}\).

  You can then have:

  \[\begin{align} & \min  ~~z \\ \notag & \mbox{s.t:}~~  zy = x \end{align}\]

  Best regards,

  Maliheh

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  Nipun Tulsian

  2025年12月30日 09:54

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  How can we model this constraints?

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  Marika Karbstein

  • Gurobi Staff

  2025年12月30日 11:18

  Can you give more details about what exactly is unclear to you?

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  Nipun Tulsian

  2025年12月30日 11:55

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  I am trying to solve f(x) = (xTAx)/B^Tx, so basically a quadratic/linear. To solve this I used the following code:                        m = gp.Model("Fractional model", env=env)
                     m.Params.NonConvex = 2

                     x = m.addMVar(len(B), lb=-0.1, ub=0.1, vtype=GRB.CONTINUOUS, name="x")
                     y = m.addVar(lb = -1000 , ub = 1000 ,vtype = GRB.CONTINUOUS, name = 'y')

                     denominator = B @ x
                     numerator = x @ A @ x

                     m.addConstr(y * denominator == numerator, name="Auxillary Constraint")
                     m.setObjective(y , gp.GRB.MINIMIZE)

                     m.optimize()
  
  I am running the above code on multiple datasets, for some I am able to get values for x but for many datasets it gives nan values for output. If I am keeping y unbounded then for all datasets its coming nan. Can you please help on how to overcome this problem

   

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  Marika Karbstein

  • Gurobi Staff

  2025年12月30日 12:54

  Does it really show “nan” or are the x values simply 0? 
  Please note that the default lower bound for all variables created in Gurobi is 0.

  I would recommend to write and check the LP-file. You can use model.write("Test.lp") before calling optimize.
  Does the LP file represent the model you want to solve?

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  Nipun Tulsian

  2025年12月31日 00:47

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  Yes it shows all nan for variables we are trying to optimize. I will check the LP file

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