Decision Optimization

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Quadratic soft constraint

  • 1.  Quadratic soft constraint

    Posted 3 days ago
    Edited by Michael Han 3 days ago
    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
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  • 2.  RE: Quadratic soft constraint

    Posted 2 days ago
    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
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  • 3.  RE: Quadratic soft constraint

    Posted 2 days ago
    Thanks for your thoughts Christian!

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