Supplying a vector of inequalities/constraints to mystic

I am trying to supply constraints to a a function minimisation that I have hitherto been performing successfully with an unconstrained algorithm available via scipy (scipy.optimize.fmin_l_bfgs_b()).

Reading up (see, e.g, Python constrained non-linear optimization), I discovered a minimisation packed called mystic that seems to be what I need. My situation is as follows. I have a function of 3N variables (representing xyz position coordinates of N nodes), and I want to supply a list of constraints such that z/x = const. for each node. This makes for a total of N constraints. How do I do define/supply these constraints most efficiently for mystic()? Can the same constraint object be used with scipy.optimize.slsqp() as well? Since my constraints are linear, this should be a viable option too.

I tried the following, but it crashed my computer:

import mystic.symbolic as ms
ieqns = ''
for p in range(N):
 ieqns += 'x'+str(p+2) +'/x'+str(p) +" <= 2"

cf = ms.generate_constraint(ms.generate_solvers(ms.simplify(ieqns)))
pf = ms.generate_penalty(ms.generate_conditions(ieqns), k=1e12)

edited Nov 13 '18 at 4:47

asked Nov 13 '18 at 4:38

ap21

184110

For N=3 I get 'x2/x0 <= 2x3/x1 <= 2x4/x2 <= 2'. Do you need a linebreak here? Also, this might indeed be suitable for a linear programming solver, as you can rewrite all your constraints to z = c * x (but we don't know your objective function...).
– Cleb
Nov 13 '18 at 7:34

@Cleb, Indeed, I realised that my objective function, though complicated, is quadratic in x. Hence, something like SLSQP should be ideal for what I am searching (see stackoverflow.com/questions/52001922/… for a guide to defining constraints with scipy.minimize()). However, for future reference, I would still like to know how to define a vector of constraints for mystic. Is adding a n enough?
– ap21
Nov 13 '18 at 17:29

@ap21: The answer is yes, adding the n is enough. Also what simplify does is isolate a single variable on the left-hand side... that can take some time, so generally, if it's as easy as your constraints equations are, I just would rewrite them by hand.
– Mike McKerns
Nov 14 '18 at 13:27

add a comment |

I tried the following, but it crashed my computer:

import mystic.symbolic as ms
ieqns = ''
for p in range(N):
 ieqns += 'x'+str(p+2) +'/x'+str(p) +" <= 2"

cf = ms.generate_constraint(ms.generate_solvers(ms.simplify(ieqns)))
pf = ms.generate_penalty(ms.generate_conditions(ieqns), k=1e12)

edited Nov 13 '18 at 4:47

asked Nov 13 '18 at 4:38

ap21

184110

For N=3 I get 'x2/x0 <= 2x3/x1 <= 2x4/x2 <= 2'. Do you need a linebreak here? Also, this might indeed be suitable for a linear programming solver, as you can rewrite all your constraints to z = c * x (but we don't know your objective function...).
– Cleb
Nov 13 '18 at 7:34

@Cleb, Indeed, I realised that my objective function, though complicated, is quadratic in x. Hence, something like SLSQP should be ideal for what I am searching (see stackoverflow.com/questions/52001922/… for a guide to defining constraints with scipy.minimize()). However, for future reference, I would still like to know how to define a vector of constraints for mystic. Is adding a n enough?
– ap21
Nov 13 '18 at 17:29

@ap21: The answer is yes, adding the n is enough. Also what simplify does is isolate a single variable on the left-hand side... that can take some time, so generally, if it's as easy as your constraints equations are, I just would rewrite them by hand.
– Mike McKerns
Nov 14 '18 at 13:27

add a comment |

I tried the following, but it crashed my computer:

import mystic.symbolic as ms
ieqns = ''
for p in range(N):
 ieqns += 'x'+str(p+2) +'/x'+str(p) +" <= 2"

cf = ms.generate_constraint(ms.generate_solvers(ms.simplify(ieqns)))
pf = ms.generate_penalty(ms.generate_conditions(ieqns), k=1e12)

edited Nov 13 '18 at 4:47

asked Nov 13 '18 at 4:38

ap21

184110

I tried the following, but it crashed my computer:

import mystic.symbolic as ms
ieqns = ''
for p in range(N):
 ieqns += 'x'+str(p+2) +'/x'+str(p) +" <= 2"

cf = ms.generate_constraint(ms.generate_solvers(ms.simplify(ieqns)))
pf = ms.generate_penalty(ms.generate_conditions(ieqns), k=1e12)

python optimization scipy mystic

edited Nov 13 '18 at 4:47

asked Nov 13 '18 at 4:38

ap21

184110

edited Nov 13 '18 at 4:47

asked Nov 13 '18 at 4:38

ap21

184110

edited Nov 13 '18 at 4:47

asked Nov 13 '18 at 4:38

ap21

184110

asked Nov 13 '18 at 4:38

ap21

184110

asked Nov 13 '18 at 4:38

ap21

184110

For N=3 I get 'x2/x0 <= 2x3/x1 <= 2x4/x2 <= 2'. Do you need a linebreak here? Also, this might indeed be suitable for a linear programming solver, as you can rewrite all your constraints to z = c * x (but we don't know your objective function...).
– Cleb
Nov 13 '18 at 7:34

@Cleb, Indeed, I realised that my objective function, though complicated, is quadratic in x. Hence, something like SLSQP should be ideal for what I am searching (see stackoverflow.com/questions/52001922/… for a guide to defining constraints with scipy.minimize()). However, for future reference, I would still like to know how to define a vector of constraints for mystic. Is adding a n enough?
– ap21
Nov 13 '18 at 17:29

@ap21: The answer is yes, adding the n is enough. Also what simplify does is isolate a single variable on the left-hand side... that can take some time, so generally, if it's as easy as your constraints equations are, I just would rewrite them by hand.
– Mike McKerns
Nov 14 '18 at 13:27

add a comment |

For N=3 I get 'x2/x0 <= 2x3/x1 <= 2x4/x2 <= 2'. Do you need a linebreak here? Also, this might indeed be suitable for a linear programming solver, as you can rewrite all your constraints to z = c * x (but we don't know your objective function...).
– Cleb
Nov 13 '18 at 7:34

@Cleb, Indeed, I realised that my objective function, though complicated, is quadratic in x. Hence, something like SLSQP should be ideal for what I am searching (see stackoverflow.com/questions/52001922/… for a guide to defining constraints with scipy.minimize()). However, for future reference, I would still like to know how to define a vector of constraints for mystic. Is adding a n enough?
– ap21
Nov 13 '18 at 17:29

@ap21: The answer is yes, adding the n is enough. Also what simplify does is isolate a single variable on the left-hand side... that can take some time, so generally, if it's as easy as your constraints equations are, I just would rewrite them by hand.
– Mike McKerns
Nov 14 '18 at 13:27

For N=3 I get 'x2/x0 <= 2x3/x1 <= 2x4/x2 <= 2'. Do you need a linebreak here? Also, this might indeed be suitable for a linear programming solver, as you can rewrite all your constraints to z = c * x (but we don't know your objective function...).
– Cleb
Nov 13 '18 at 7:34

@Cleb, Indeed, I realised that my objective function, though complicated, is quadratic in x. Hence, something like SLSQP should be ideal for what I am searching (see stackoverflow.com/questions/52001922/… for a guide to defining constraints with scipy.minimize()). However, for future reference, I would still like to know how to define a vector of constraints for mystic. Is adding a n enough?
– ap21
Nov 13 '18 at 17:29

@ap21: The answer is yes, adding the n is enough. Also what simplify does is isolate a single variable on the left-hand side... that can take some time, so generally, if it's as easy as your constraints equations are, I just would rewrite them by hand.
– Mike McKerns
Nov 14 '18 at 13:27

add a comment |

1 Answer
1

active

oldest

votes

I'm the mystic author. I believe what you are looking to do is something like this:

>>> import mystic.symbolic as ms
>>> ieqns = ''
>>> for p in range(10):
... ieqns += 'x0 <= 2*x1n'.format(p+2,p)
... 
>>> cf = ms.generate_constraint(ms.generate_solvers(ieqns))
>>>
>>> # test that it applies the constraints
>>> cf([1.,3.,5.,7.,9.,11.,13.,15.,17.,19.,21.,23.,25.])
[1.0, 3.0, 2.0, 6.0, 4.0, 11.0, 8.0, 15.0, 16.0, 19.0, 21.0, 23.0, 25.0]

Then we can minimize while applying the constraints (however, in the following case the constraints are basically irrelevant):

>>> # get an objective
>>> import mystic.models as mm
>>> rosen = mm.dejong.Rosenbrock(12).function
>>> 
>>> # get an optimizer
>>> import mystic.solvers as my
>>> result = my.diffev2(rosen, x0=bounds, bounds=bounds, constrints=cf, npop=40, disp=False, full_output=True, gtol=100)
>>>
>>> # get the solution 
>>> result[0]
array([0.99997179, 1.00005506, 1.00012367, 0.99998539, 0.99984306,
 0.99981495, 0.999951 , 0.99996505, 0.99971107, 0.99925239,
 0.99846259, 0.99692293])
>>> # and the final 'cost'
>>> result[1]
2.2385442425350018e-05
>>>

answered Nov 14 '18 at 4:24

Mike McKerns

17.6k46789

Thanks! But tell me, shouldn't suppyling a vector x to the constraints give back a vector of Boolean values? What are the numbers it is returning?
– ap21
Nov 14 '18 at 21:57

A different question: I have an explicit gradient of my cost function as well. I couldn't find any default algorithm in mystic that makes use of an explicit gradient. Is there some algorithm that can use a gradient?
– ap21
Nov 14 '18 at 22:03

1

@ap21: No, a mystic.constraint is a "mapping", so it has the form x' = c(x) -- you could think of it as a nonlinear transform. On the other hand, a mystic.penalty returns a penalty value that is added to the cost... so has the form y = k*p(x), which is additive to the cost. With respect to your second question, the most recent mystic release doesn't have a gradient solver... however, I have built a gradient solver, and standalone functions that calculate the gradient from points the solar evaluates. These will be included in the next release, and should be in GitHub this month.
– Mike McKerns
Nov 15 '18 at 0:58

add a comment |

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1 Answer
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active

oldest

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1 Answer
1

active

oldest

votes

I'm the mystic author. I believe what you are looking to do is something like this:

>>> import mystic.symbolic as ms
>>> ieqns = ''
>>> for p in range(10):
... ieqns += 'x0 <= 2*x1n'.format(p+2,p)
... 
>>> cf = ms.generate_constraint(ms.generate_solvers(ieqns))
>>>
>>> # test that it applies the constraints
>>> cf([1.,3.,5.,7.,9.,11.,13.,15.,17.,19.,21.,23.,25.])
[1.0, 3.0, 2.0, 6.0, 4.0, 11.0, 8.0, 15.0, 16.0, 19.0, 21.0, 23.0, 25.0]

Then we can minimize while applying the constraints (however, in the following case the constraints are basically irrelevant):

>>> # get an objective
>>> import mystic.models as mm
>>> rosen = mm.dejong.Rosenbrock(12).function
>>> 
>>> # get an optimizer
>>> import mystic.solvers as my
>>> result = my.diffev2(rosen, x0=bounds, bounds=bounds, constrints=cf, npop=40, disp=False, full_output=True, gtol=100)
>>>
>>> # get the solution 
>>> result[0]
array([0.99997179, 1.00005506, 1.00012367, 0.99998539, 0.99984306,
 0.99981495, 0.999951 , 0.99996505, 0.99971107, 0.99925239,
 0.99846259, 0.99692293])
>>> # and the final 'cost'
>>> result[1]
2.2385442425350018e-05
>>>

answered Nov 14 '18 at 4:24

Mike McKerns

17.6k46789

Thanks! But tell me, shouldn't suppyling a vector x to the constraints give back a vector of Boolean values? What are the numbers it is returning?
– ap21
Nov 14 '18 at 21:57

A different question: I have an explicit gradient of my cost function as well. I couldn't find any default algorithm in mystic that makes use of an explicit gradient. Is there some algorithm that can use a gradient?
– ap21
Nov 14 '18 at 22:03

1

@ap21: No, a mystic.constraint is a "mapping", so it has the form x' = c(x) -- you could think of it as a nonlinear transform. On the other hand, a mystic.penalty returns a penalty value that is added to the cost... so has the form y = k*p(x), which is additive to the cost. With respect to your second question, the most recent mystic release doesn't have a gradient solver... however, I have built a gradient solver, and standalone functions that calculate the gradient from points the solar evaluates. These will be included in the next release, and should be in GitHub this month.
– Mike McKerns
Nov 15 '18 at 0:58

add a comment |

I'm the mystic author. I believe what you are looking to do is something like this:

>>> import mystic.symbolic as ms
>>> ieqns = ''
>>> for p in range(10):
... ieqns += 'x0 <= 2*x1n'.format(p+2,p)
... 
>>> cf = ms.generate_constraint(ms.generate_solvers(ieqns))
>>>
>>> # test that it applies the constraints
>>> cf([1.,3.,5.,7.,9.,11.,13.,15.,17.,19.,21.,23.,25.])
[1.0, 3.0, 2.0, 6.0, 4.0, 11.0, 8.0, 15.0, 16.0, 19.0, 21.0, 23.0, 25.0]

Then we can minimize while applying the constraints (however, in the following case the constraints are basically irrelevant):

>>> # get an objective
>>> import mystic.models as mm
>>> rosen = mm.dejong.Rosenbrock(12).function
>>> 
>>> # get an optimizer
>>> import mystic.solvers as my
>>> result = my.diffev2(rosen, x0=bounds, bounds=bounds, constrints=cf, npop=40, disp=False, full_output=True, gtol=100)
>>>
>>> # get the solution 
>>> result[0]
array([0.99997179, 1.00005506, 1.00012367, 0.99998539, 0.99984306,
 0.99981495, 0.999951 , 0.99996505, 0.99971107, 0.99925239,
 0.99846259, 0.99692293])
>>> # and the final 'cost'
>>> result[1]
2.2385442425350018e-05
>>>

answered Nov 14 '18 at 4:24

Mike McKerns

17.6k46789

Thanks! But tell me, shouldn't suppyling a vector x to the constraints give back a vector of Boolean values? What are the numbers it is returning?
– ap21
Nov 14 '18 at 21:57

A different question: I have an explicit gradient of my cost function as well. I couldn't find any default algorithm in mystic that makes use of an explicit gradient. Is there some algorithm that can use a gradient?
– ap21
Nov 14 '18 at 22:03

1

@ap21: No, a mystic.constraint is a "mapping", so it has the form x' = c(x) -- you could think of it as a nonlinear transform. On the other hand, a mystic.penalty returns a penalty value that is added to the cost... so has the form y = k*p(x), which is additive to the cost. With respect to your second question, the most recent mystic release doesn't have a gradient solver... however, I have built a gradient solver, and standalone functions that calculate the gradient from points the solar evaluates. These will be included in the next release, and should be in GitHub this month.
– Mike McKerns
Nov 15 '18 at 0:58

add a comment |

I'm the mystic author. I believe what you are looking to do is something like this:

>>> import mystic.symbolic as ms
>>> ieqns = ''
>>> for p in range(10):
... ieqns += 'x0 <= 2*x1n'.format(p+2,p)
... 
>>> cf = ms.generate_constraint(ms.generate_solvers(ieqns))
>>>
>>> # test that it applies the constraints
>>> cf([1.,3.,5.,7.,9.,11.,13.,15.,17.,19.,21.,23.,25.])
[1.0, 3.0, 2.0, 6.0, 4.0, 11.0, 8.0, 15.0, 16.0, 19.0, 21.0, 23.0, 25.0]

Then we can minimize while applying the constraints (however, in the following case the constraints are basically irrelevant):

>>> # get an objective
>>> import mystic.models as mm
>>> rosen = mm.dejong.Rosenbrock(12).function
>>> 
>>> # get an optimizer
>>> import mystic.solvers as my
>>> result = my.diffev2(rosen, x0=bounds, bounds=bounds, constrints=cf, npop=40, disp=False, full_output=True, gtol=100)
>>>
>>> # get the solution 
>>> result[0]
array([0.99997179, 1.00005506, 1.00012367, 0.99998539, 0.99984306,
 0.99981495, 0.999951 , 0.99996505, 0.99971107, 0.99925239,
 0.99846259, 0.99692293])
>>> # and the final 'cost'
>>> result[1]
2.2385442425350018e-05
>>>

answered Nov 14 '18 at 4:24

Mike McKerns

17.6k46789

I'm the mystic author. I believe what you are looking to do is something like this:

>>> import mystic.symbolic as ms
>>> ieqns = ''
>>> for p in range(10):
... ieqns += 'x0 <= 2*x1n'.format(p+2,p)
... 
>>> cf = ms.generate_constraint(ms.generate_solvers(ieqns))
>>>
>>> # test that it applies the constraints
>>> cf([1.,3.,5.,7.,9.,11.,13.,15.,17.,19.,21.,23.,25.])
[1.0, 3.0, 2.0, 6.0, 4.0, 11.0, 8.0, 15.0, 16.0, 19.0, 21.0, 23.0, 25.0]

Then we can minimize while applying the constraints (however, in the following case the constraints are basically irrelevant):

>>> # get an objective
>>> import mystic.models as mm
>>> rosen = mm.dejong.Rosenbrock(12).function
>>> 
>>> # get an optimizer
>>> import mystic.solvers as my
>>> result = my.diffev2(rosen, x0=bounds, bounds=bounds, constrints=cf, npop=40, disp=False, full_output=True, gtol=100)
>>>
>>> # get the solution 
>>> result[0]
array([0.99997179, 1.00005506, 1.00012367, 0.99998539, 0.99984306,
 0.99981495, 0.999951 , 0.99996505, 0.99971107, 0.99925239,
 0.99846259, 0.99692293])
>>> # and the final 'cost'
>>> result[1]
2.2385442425350018e-05
>>>

answered Nov 14 '18 at 4:24

Mike McKerns

17.6k46789

answered Nov 14 '18 at 4:24

Mike McKerns

17.6k46789

answered Nov 14 '18 at 4:24

Mike McKerns

17.6k46789

answered Nov 14 '18 at 4:24

Mike McKerns

17.6k46789

Thanks! But tell me, shouldn't suppyling a vector x to the constraints give back a vector of Boolean values? What are the numbers it is returning?
– ap21
Nov 14 '18 at 21:57

A different question: I have an explicit gradient of my cost function as well. I couldn't find any default algorithm in mystic that makes use of an explicit gradient. Is there some algorithm that can use a gradient?
– ap21
Nov 14 '18 at 22:03

1

@ap21: No, a mystic.constraint is a "mapping", so it has the form x' = c(x) -- you could think of it as a nonlinear transform. On the other hand, a mystic.penalty returns a penalty value that is added to the cost... so has the form y = k*p(x), which is additive to the cost. With respect to your second question, the most recent mystic release doesn't have a gradient solver... however, I have built a gradient solver, and standalone functions that calculate the gradient from points the solar evaluates. These will be included in the next release, and should be in GitHub this month.
– Mike McKerns
Nov 15 '18 at 0:58

add a comment |

Thanks! But tell me, shouldn't suppyling a vector x to the constraints give back a vector of Boolean values? What are the numbers it is returning?
– ap21
Nov 14 '18 at 21:57

A different question: I have an explicit gradient of my cost function as well. I couldn't find any default algorithm in mystic that makes use of an explicit gradient. Is there some algorithm that can use a gradient?
– ap21
Nov 14 '18 at 22:03

1

@ap21: No, a mystic.constraint is a "mapping", so it has the form x' = c(x) -- you could think of it as a nonlinear transform. On the other hand, a mystic.penalty returns a penalty value that is added to the cost... so has the form y = k*p(x), which is additive to the cost. With respect to your second question, the most recent mystic release doesn't have a gradient solver... however, I have built a gradient solver, and standalone functions that calculate the gradient from points the solar evaluates. These will be included in the next release, and should be in GitHub this month.
– Mike McKerns
Nov 15 '18 at 0:58

Thanks! But tell me, shouldn't suppyling a vector x to the constraints give back a vector of Boolean values? What are the numbers it is returning?
– ap21
Nov 14 '18 at 21:57

A different question: I have an explicit gradient of my cost function as well. I couldn't find any default algorithm in mystic that makes use of an explicit gradient. Is there some algorithm that can use a gradient?
– ap21
Nov 14 '18 at 22:03

@ap21: No, a mystic.constraint is a "mapping", so it has the form x' = c(x) -- you could think of it as a nonlinear transform. On the other hand, a mystic.penalty returns a penalty value that is added to the cost... so has the form y = k*p(x), which is additive to the cost. With respect to your second question, the most recent mystic release doesn't have a gradient solver... however, I have built a gradient solver, and standalone functions that calculate the gradient from points the solar evaluates. These will be included in the next release, and should be in GitHub this month.
– Mike McKerns
Nov 15 '18 at 0:58

add a comment |

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