Decision Optimization

 View Only

  • 1.  Quadratic soft constraint

    Posted Wed June 09, 2021 07:58 PM
    Edited by System Fri January 20, 2023 04:12 PM
    Suppose I have a problem 
    min
      f(x)
    Subject To
      h(x) <= 0
    To make h(x) a quadratic soft constraint, we could add: 
    min
      f(x) + λ*s^2
    Subject To
      h(x) - s <= 0
      s >= 0
    or  
    min
      f(x) + λ*t
    Subject To
      h(x) - s <= 0
      s^2 <= t
      s, t >= 0
    Is there any reason a priori to believe one formulation will be superior in terms of CPLEX performance or stability?

    Thanks.

    ------------------------------
    Michael Han
    ------------------------------
    #DecisionOptimization


  • 2.  RE: Quadratic soft constraint

    Posted Thu June 10, 2021 06:15 AM
    Hi Michael,

    Internally CPLEX transforms (mi)qcp into (mi)socp models. So if you provide the first formulation, it will actually be transformed into something close to the second formulation. It therefore probably will not make much of a difference which one you give to CPLEX.

    Christian.

    ------------------------------
    Christian Bliek
    ------------------------------

    Original Message


  • 3.  RE: Quadratic soft constraint

    Posted Thu June 10, 2021 04:05 PM
    Thanks for your thoughts Christian!

    ------------------------------
    Michael Han
    ------------------------------

    Original Message