Mpec Examples
Apps.MpecExamples History
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!!! Maximum Selector
* %list list-page%
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'''GEKKO MIN function (min2)'''
See [[https://gekko.readthedocs.io/en/latest/examples.html|GEKKO Documentation]] for additional examples.
See [[https://gekko.readthedocs.io/en/latest/examples.html|GEKKO Documentation]] for additional examples.
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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:)
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))
'''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))
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!!! Absolute Value
* %list list-page%
to:
'''GEKKO SIGNUM function (sign2)'''
See [[https://gekko.readthedocs.io/en/latest/examples.html|GEKKO Documentation]] for additional examples.
See [[https://gekko.readthedocs.io/en/latest/examples.html|GEKKO Documentation]] for additional examples.
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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:)
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()
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m.solve() # solve
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Model
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Model
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%width=50px%Attach:apm.png [[Main/Objects|APMonitor Objects]]
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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:)
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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. [[https://www.sciencedirect.com/science/article/pii/S036054421631814X|Article]]
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]]
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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]]
* 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]]
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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
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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:)
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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:)
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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:)
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! y = x if the corresponding element of X is greater than zero
! y = -x if the corresponding element of X isless than zero
! y = -x if the corresponding element of X is
to:
! y = x if the corresponding element of X is > than zero
! y = -x if the corresponding element of X is < than zero
! y = -x if the corresponding element of X is < than zero
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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'
! 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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End Objects
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to:
End Connections
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End Parameters
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End Variables
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Parameters
Variables
s_a >
Equations
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
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:)
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----
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----
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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.
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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.
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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
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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
! 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
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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
* %list list-page% [[Attach:min.apm | MIN Operator Example]]
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!!! MPEC examples
----
!!!! SIGN Operator
* %list list-page% [[Attach:sign.apm | Download SIGN Operator Example]]
!!!! SIGN Operator
* %list list-page% [[Attach:sign.apm | Download
to:
!!! SIGN Operator
* %list list-page% [[Attach:sign.apm | SIGN Operator Example]]
* %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]]
(:html:)<font size=1><pre>
</pre></font>(:htmlend:)
----
* %list list-page% [[Attach:abs.apm | ABS Operator Example]]
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</pre></font>(:htmlend:)
----
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----
!!!! SIGN Operator
* %list list-page% [[Attach:sign.apm | Download SIGN Operator Example]]
!!!! SIGN Operator
* %list list-page% [[Attach:sign.apm | Download SIGN Operator Example]]
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</pre></font>(:htmlend:)
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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:)
----
! 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:)
----
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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>
</pre></font>(:htmlend:)
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]]
----
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</pre></font>(:htmlend:)