Apps

Mpec Examples

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
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!!! Maximum Selector (MAX) Operator

* %list list-page% [[Attach:max.apm | MAX Operator Example]]

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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
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!!! Minimum Selector (MIN) Operator

* %list list-page% [[Attach:min.apm | MIN Operator Example]]
September 24, 2009, at 08:45 PM by 206.180.155.75 -
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!!! MPEC examples

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!!!! SIGN Operator

* %list list-page% [[Attach:sign.apm | Download
SIGN Operator Example]]
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!!! SIGN Operator

* %list list
-page% [[Attach:sign.apm | SIGN Operator Example]]
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!!! Absolute Value (ABS) Operator

* %list list-page% [[Attach:abs.apm | ABS Operator Example]]

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September 24, 2009, at 08:41 PM by 206.180.155.75 -
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* %list list-page% [[Attach:sign.apm | SIGN Operator]]
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!!!! SIGN
Operator

* %list list-page% [[Attach:sign.apm | Download SIGN Operator Example
]]
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
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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.

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!!! MPEC examples

* %list list-page% [[Attach:sign.apm | SIGN Operator]]

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