#! /usr/bin/env python3
#
def himmelblau_minimize ( ):

#*****************************************************************************80
#
## himmelblau_minimize() seeks a minimizer of the Himmelblau function.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    04 March 2023
#
#  Author:
#
#    John Burkardt
#
  import numpy as np
  from scipy.optimize import minimize

  print ( '' )
  print ( 'himmelblau_minimize():' )
  print ( '  Seek a minimizer of the Himmelblau function.' )

  start = np.array ( [ 0.0, 0.0 ] )
  print ( '  Starting at x = ', start )
  print ( '  f(x) = ', himmelblau ( start ) )

  result = minimize ( himmelblau, start )

  print ( '' )
  print ( '  Minimizer found at ', result.x )
  print ( '  f(x) = ', himmelblau ( result.x ) )

  return

def himmelblau ( x ):  
  f = ( x[0]**2 + x[1] - 11.0 )**2 + ( x[0] + x[1]**2 - 7.0 )**2
  return f

if ( __name__ == '__main__' ):
  himmelblau_minimize ( )