Apps

Mpec Examples

Apps.MpecExamples History

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February 14, 2019, at 03:04 PM by 10.37.111.106 -
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----

!!! Maximum Selector
(MAX) Operator

* %list list-page%
[[Attach:max.apm | MAX Operator Example]]
to:
'''GEKKO MIN function (min2)'''

See
[[https://gekko.readthedocs.io/en/latest/examples.html|GEKKO Documentation]] for additional examples.
Added lines 206-224:
from gekko import GEKKO
m = GEKKO()
x1 = m.Param(-2)
x2 = m.Param(-1)
# use min2
y = m.min2(x1,x2)
m.solve() # solve
print('x1: ' + str(x1.value))
print('x2: ' + str(x2.value))
print('y: '  + str(y.value))
(:sourceend:)

----

!!! Maximum Selector (MAX) Operator

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

(:source lang=python:)
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(:sourceend:)

'''GEKKO MAX function (min2)'''

See [[https://gekko.readthedocs.io/en/latest/examples.html|GEKKO Documentation]] for additional examples.

(:source lang=python:)
from gekko import GEKKO
m = GEKKO()
x1 = m.Param(-2)
x2 = m.Param(-1)
# use max2
y = m.max2(x1,x2)
m.solve() # solve
print('x1: ' + str(x1.value))
print('x2: ' + str(x2.value))
print('y: '  + str(y.value))
February 14, 2019, at 02:17 PM by 10.37.111.106 -
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----

!!! Absolute Value
(ABS) Operator

* %list list-page%
[[Attach:abs.apm | ABS Operator Example]]
to:
'''GEKKO SIGNUM function (sign2)'''

See
[[https://gekko.readthedocs.io/en/latest/examples.html|GEKKO Documentation]] for additional examples.
Added lines 64-80:
from gekko import GEKKO
m = GEKKO()
x = m.Param(-2)
# use sign2 to define a new variable
y = m.sign2(x)
m.solve()  # solve
print('x: ' + str(x.value))
print('y: ' + str(y.value))
(:sourceend:)

----

!!! Absolute Value (ABS) Operator

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

(:source lang=python:)
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# solve

m.solve()
to:
m.solve() # solve
February 14, 2019, at 02:05 PM by 10.37.111.106 -
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Model signum
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Model
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Model signum
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Model
February 14, 2019, at 01:28 PM by 10.37.111.106 -
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%width=50px%Attach:apm.png [[Main/Objects|APMonitor Objects]]
February 14, 2019, at 01:16 PM by 10.37.111.106 -
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February 12, 2019, at 03:23 PM by 10.37.233.114 -
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'''GEKKO ABS function (abs2)'''

See [[https://gekko.readthedocs.io/en/latest/examples.html|GEKKO Documentation]] for additional examples.

(:source lang=python:)
from gekko import GEKKO

m = GEKKO()
x = m.Param(-2)
# use abs2 to define a new variable
y = m.abs2(x)
# use abs2 in an equation
z = m.Var()
m.Equation(z==m.abs2(x)+1)

# solve
m.solve()

print('x: ' + str(x.value))
print('y: ' + str(y.value))
print('z: ' + str(z.value))
(:sourceend:)
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. [[https://www.sciencedirect.com/science/article/pii/S036054421631814X|Article]]
to:
!!!! 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. [[https://www.sciencedirect.com/science/article/pii/S036054421631814X|Article]]
July 20, 2017, at 01:49 AM by 144.5.226.51 -
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----
to:
----

* 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. [[https://www.sciencedirect.com/science/article/pii/S036054421631814X|Article]]
July 20, 2017, at 01:47 AM by 144.5.226.51 -
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! SIGN function as an Object
to:
! SIGN function MPEC as an Object
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! ABS function as an Object
to:
! 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
to:
! SIGN function as an Object
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! MPEC formulation for ABS function using an object
to:
! 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 -
Added lines 36-57:


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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 -
Changed lines 45-46 from:
!    y = x if the corresponding element of X is greater than zero
!    y = -x if the corresponding element of X is less than zero
to:
!    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'
to:
! MPEC formulation for ABS function using an object
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to:
End Objects
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to:
End Connections
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to:
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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to:
----
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.
to:
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.
to:
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
to:
   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

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

(: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 -
Added lines 41-72:

(: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

* %list list-page% [[Attach:min.apm | MIN Operator Example]]
September 25, 2009, at 02:45 AM by 206.180.155.75 -
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!!! MPEC examples

----

!!!! SIGN Operator

* %list list-page% [[Attach:sign.apm | Download
SIGN Operator Example]]
to:
!!! 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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</pre></font>(:htmlend:)
----
September 25, 2009, at 02:41 AM by 206.180.155.75 -
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* %list list-page% [[Attach:sign.apm | SIGN Operator]]
to:
----

!!!! SIGN
Operator

* %list list-page% [[Attach:sign.apm | Download SIGN Operator Example
]]
September 25, 2009, at 02:39 AM by 206.180.155.75 -
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----
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to:
! 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

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

----

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

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