Apps.MpecExamples History

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March 06, 2010, at 02:44 AM by 206.180.155.75 -
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October 09, 2009, at 12:13 PM by 158.35.225.227 -
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Mathematical Programs with Equilibrium Constraints (MPECs) are formulations that can be used to model certain classes of discrete events. MPECs can be more efficient than solving mixed integer formulations of the optimization problems.

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Mathematical Programs with Equilibrium Constraints (MPECs) are formulations that can be used to model certain classes of discrete events. MPECs can be more efficient than solving mixed integer formulations of the optimization problems because it avoids the combinatorial difficulties of searching for optimal discrete variables.

October 09, 2009, at 12:12 PM by 158.35.225.227 -
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Mathematical Programs with Equilibrium Constraints (MPECs) are formulations that can be used to model certain classes of discrete events. MPECs can be more efficient than solving mixed integer problems.

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Mathematical Programs with Equilibrium Constraints (MPECs) are formulations that can be used to model certain classes of discrete events. MPECs can be more efficient than solving mixed integer formulations of the optimization problems.

October 09, 2009, at 12:10 PM by 158.35.225.227 -
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Model signum

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Model sign

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Model signum

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Model abs

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    y = x1 + s_a
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    y = x1 - s_a
September 24, 2009, at 09:01 PM by 206.180.155.75 -
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MPEC formulation for MIN function

y = MIN(x1,x2) returns a value y, where:

y = x1 if x1 < x2

y = x2 if x2 < x1

Model signum

  Parameters
    x1 = -2
    x2 = -1
  End Parameters

  Variables
    y

    ! slack variables
    s_a >= 0
    s_b >= 0
  End Variables

  Equations
    ! test min operator, y = min(x1,x2)
    x2 - x1 = s_b - s_a
    y = x1 + s_a

    minimize s_a*s_b
  End Equations

End Model </pre></font>(:htmlend:)


Maximum Selector (MAX) Operator

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MPEC formulation for MAX function

y = MAX(x1,x2) returns a value y, where:

y = x1 if x1 > x2

y = x2 if x2 > x1

Model signum

  Parameters
    x1 = -2
    x2 = 4
  End Parameters

  Variables
    y

    ! slack variables
    s_a >= 0
    s_b >= 0
  End Variables

  Equations
    ! test max operator, y = max(x1,x2)
    x2 - x1 = s_a - s_b
    y = x1 + s_a

    minimize s_a*s_b
  End Equations

End Model

September 24, 2009, at 08:51 PM by 206.180.155.75 -
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MPEC formulation for ABS function

y = ABS(x) returns a value y, where:

y = x if the corresponding element of X is greater than zero

y = -x if the corresponding element of X is less than zero

Model signum

  Parameters
    x = -2
  End Parameters

  Variables
    y

    s_a >= 0
    s_b >= 0
  End Variables

  Equations
    ! test abs operator, y = abs(x)
    x = s_b - s_a
    y = s_a + s_b

    minimize s_a*s_b
  End Equations

End Model </pre></font>(:htmlend:)


Minimum Selector (MIN) Operator

September 24, 2009, at 08:45 PM by 206.180.155.75 -
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MPEC examples


SIGN Operator

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SIGN Operator

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Absolute Value (ABS) Operator

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September 24, 2009, at 08:41 PM by 206.180.155.75 -
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September 24, 2009, at 08:39 PM by 206.180.155.75 -
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MPEC formulation for SIGN function

y = SIGN(x) returns a value y, where:

1 if the corresponding element of X is greater than zero

-1 if the corresponding element of X is less than zero

Model signum

  Parameters
    x = -2
  End Parameters

  Variables
    y >= -1, <= 1

    s_a >= 0
    s_b >= 0
  End Variables

  Equations
    ! test sign operator, y = sign(x)
    x = s_b - s_a

    minimize s_a*(1+y) + s_b*(1-y)
  End Equations

End Model </pre></font>(:htmlend:)


September 23, 2009, at 10:15 PM by 206.180.155.75 -
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MPEC: Mathematical Programs with Equilibrium Constraints

Mathematical Programs with Equilibrium Constraints (MPECs) are formulations that can be used to model certain classes of discrete events. MPECs can be more efficient than solving mixed integer problems.


MPEC examples


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