Apps

Mpec Examples

Apps.MpecExamples History

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July 20, 2017, at 01:49 AM by 144.5.226.51 -
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  • Mojica, J.L., Petersen, D.J., Hansen, B., Powell, K.M., Hedengren, J.D., Optimal Combined Long-Term Facility Design and Short-Term Operational Strategy for CHP Capacity Investments, Energy, Vol 118, 1 January 2017, pp. 97–115. Article
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Reference

Mojica, J.L., Petersen, D.J., Hansen, B., Powell, K.M., Hedengren, J.D., Optimal Combined Long-Term Facility Design and Short-Term Operational Strategy for CHP Capacity Investments, Energy, Vol 118, 1 January 2017, pp. 97–115. Article

July 20, 2017, at 01:49 AM by 144.5.226.51 -
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  • Mojica, J.L., Petersen, D.J., Hansen, B., Powell, K.M., Hedengren, J.D., Optimal Combined Long-Term Facility Design and Short-Term Operational Strategy for CHP Capacity Investments, Energy, Vol 118, 1 January 2017, pp. 97–115. Article
July 20, 2017, at 01:47 AM by 144.5.226.51 -
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SIGN function as an Object

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SIGN function MPEC as an Object

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ABS function as an Object

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ABS function MPEC as an Object

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MIN function MPEC as an Object

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MAX function MPEC as an Object

July 20, 2017, at 01:46 AM by 144.5.226.51 -
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SIGN function with Object

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SIGN function as an Object

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MPEC formulation for ABS function using an object

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ABS function as an Object

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(:html:)<font size=2><pre> Objects

  f = max

End Objects

Connections

  f.x[1] = x1
  f.x[2] = x2
  f.y = y

End Connections

Parameters

  x1 = -2
  x2 =  4

End Parameters

Variables

  y

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

July 20, 2017, at 01:43 AM by 144.5.226.51 -
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(:html:)<font size=2><pre> Objects

  f = min

End Objects

Connections

  f.x[1] = x1
  f.x[2] = x2
  f.y = y

End Connections

Parameters

  x1 = -2
  x2 = -1

End Parameters

Variables

  y

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

July 20, 2017, at 01:41 AM by 144.5.226.51 -
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SIGN function with Object

Objects

  f = sign

End Objects

Connections

  f.x = x
  f.y = y

End Connections

Parameters

  x = -2

End Parameters

Variables

  y

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

July 20, 2017, at 01:37 AM by 144.5.226.51 -
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y = x if the corresponding element of X is greater than zero

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

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

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

July 20, 2017, at 01:37 AM by 144.5.226.51 -
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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

this uses the APMonitor object 'abs'

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MPEC formulation for ABS function using an object

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End Objects

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End Connections

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End Parameters

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End Variables

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July 20, 2017, at 01:22 AM by 144.5.226.51 -
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Model abs

  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

to:

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

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(:html:)<font size=2><pre>

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

this uses the APMonitor object 'abs'

Objects

  f = abs

Connections

  f.x = x
  f.y = y

Parameters

  x = -2

Variables

  y

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

March 06, 2010, at 09:44 AM by 206.180.155.75 -
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October 09, 2009, at 06:13 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 06:12 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 06:10 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 25, 2009, at 03:01 AM 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

(:html:)<font size=1><pre>

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 25, 2009, at 02:51 AM by 206.180.155.75 -
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(:html:)<font size=1><pre>

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 25, 2009, at 02:45 AM 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 25, 2009, at 02:41 AM by 206.180.155.75 -
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September 25, 2009, at 02:39 AM 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 24, 2009, at 04:15 AM 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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</pre></font>(:htmlend:)