to restrict parameter values strictly with in bounds

Question

Hi,

I am trying to optimize a function using l_bfgs constraint optimization routine in scipy. But the optimization routine passes values to the function, which are not with in the Bounds.

my full code looks like,

def humpy(aParams):
 aParams = numpy.asarray(aParams)
 print aParams
 ####
 # connect to some other software for simulation
 # data[1] & data[2] are read
 ##### objective function
 val = sum(0.5*(data[1] - data[2])**2)
 print val
 return val

 ####

def approx_fprime():
 ####
 Initial = numpy.asarray([10.0, 15.0, 50.0, 10.0])
 interval = [(5.0, 60000.0),(10.0, 50000.0),(26.0, 100000.0),(8.0, 50000.0)]

 opt = optimize.fmin_l_bfgs(humpy,Initial,fprime=approx_fprime, bounds=interval ,pgtol=1.0000000000001e-05,iprint=1, maxfun=50000)

 print 'optimized parameters',opt[0]
 print 'Optimized function value', opt[1]

####### the end ####

based on the initial values(Initial) and bounds(interval) opt = optimize.fmin_l_bfgs() will pass values to my software for simulation, but the values passed should be with in 'bounds'. Thats not the case..see below the values passed at various iterations

iter 1  = [ 10.23534209  15.1717302   50.5117245   10.28731118]

iter 2  = [ 10.23534209  15.1717302   50.01160842  10.39018429]

          [ 11.17671043  15.85865102  50.05804208  11.43655591]

          [ 11.17671043  15.85865102  50.05804208  11.43655591]

          [ 11.28847754  15.85865102  50.05804208  11.43655591]

          [ 11.17671043  16.01723753  50.05804208  11.43655591]

          [ 11.17671043  15.85865102  50.5586225   11.43655591]
          ...............
          ...............
          ...............
         [  49.84670071 -4.4139714 62.2536381 23.3155698847]

at this iteration -4.4139714 is passed to my 2nd parameter but it should vary from (10.0, 50000.0), from where come -4.4139714 i don't know?

where should i change in the code? so that it passed values which should be with in bounds

Answer 1

You are trying to do bitwise exclusive or (the ^ operator) on floats, which makes no sense, so I don't think your code is actually the code you have problems with. However, I changed the ^ to ** assuming that was what you meant, and had no problems. The code worked fine for me with that change. The parameters are restricted exactly as defined.

Python 2.5.

Answer 2

Are you asking about doing something like this?

def humpy(aParams):
  aParams = numpy.asarray(aParams)
  x = aParams[0]
  y = aParams[1]
  z = aParams[2]
  u = aParams[3]
  v = aParams[4]
  assert 2 <= x <= 50000
  assert 1 <= y <= 35000
  assert 1 <= z <= 45000
  assert 2 <= u <= 50000
  assert 2 <= v <= 60000
  val=100.0*((y-x**2.0)^2.0+(z-y**2.0)^2.0+(u-z**2.0)^2.0+(v-u**2.0)^2.0)+(1-x)^2.0+(1-y)^2.0+(1-z)^2.0+(1-u)^2.0
  return val