Source code for naginterfaces.​library.​examples.​glopt.​nlp_multistart_sqp_lsq_ex

#!/usr/bin/env python
"``naginterface.library.glopt.nlp_multistart_sqp_lsq`` Python Example."

# NAG Copyright 2017-2019.

# pylint: disable=invalid-name,too-many-arguments,too-many-locals

from math import exp
import warnings

import numpy as np

from naginterfaces.base import utils
from naginterfaces.library import glopt

[docs]def main(): """ Example for :func:`naginterfaces.library.glopt.nlp_multistart_sqp_lsq`. Global optimization of a sum of squares problem using multi-start. Demonstrates catching a ``NagAlgorithmicWarning`` and accessing its ``return_data`` attribute. >>> main() naginterfaces.library.glopt.nlp_multistart_sqp_lsq Python Example Results. Minimizes the sum of squares function based on Problem 57 in Hock and Schittkowski (1981). Solution number 1. Final objective value = 0.0142298. """ print( 'naginterfaces.library.glopt.nlp_multistart_sqp_lsq ' 'Python Example Results.' ) print('Minimizes the sum of squares function') print('based on Problem 57 in Hock and Schittkowski (1981).') # Input data for the optimizer: # The number of solutions required: nb = 1 # The number of nonlinear constraints: ncnln = 1 # The number of starting points: npts = 3 # Matrix of general linear constraints: a = np.array([[1.0, 1.0]]) # The bounds for the problem: bl = [0.4, -4., 1., 0.] bu = [1.e25]*len(bl) # Coefficients of the constant vector y of the objective function: y = [ 0.49, 0.49, 0.48, 0.47, 0.48, 0.47, 0.46, 0.46, 0.45, 0.43, 0.45, 0.43, 0.43, 0.44, 0.43, 0.43, 0.46, 0.45, 0.42, 0.42, 0.43, 0.41, 0.41, 0.40, 0.42, 0.40, 0.40, 0.41, 0.40, 0.41, 0.41, 0.40, 0.40, 0.40, 0.38, 0.41, 0.40, 0.40, 0.41, 0.38, 0.40, 0.40, 0.39, 0.39 ] def cb_confun(mode, needc, x, cjsl, nstate): """ Function to evaluate the nonlinear constraint and its first derivatives. """ if needc[0] <= 0 or mode == 1: c = [0.]*len(needc) elif mode in [0, 2]: c = [0.49*x[1] - x[0]*x[1] - 0.09] if needc[0] <= 0: return c if mode in [1, 2]: cjsl[0, 0] = -x[1] cjsl[0, 1] = -x[0] + 0.49 return c def cb_objfun(mode, needfi, x, fjsl, nstate): "This is a two-dimensional objective function." # The set of 44 'a' data values: a = [ 8., 8., 10., 10., 10., 10., 12., 12., 12., 12., 14., 14., 14., 16., 16., 16., 18., 18., 20., 20., 20., 22., 22., 22., 24., 24., 24., 26., 26., 26., 28., 28., 30., 30., 30., 32., 32., 34., 36., 36., 38., 38., 40., 42., ] m = fjsl.shape[0] f = np.empty(m) for fi in range(m): exp_term = exp(-x[1]*(a[fi] - 8.)) if needfi == fi + 1 or mode in [0, 2]: f[fi] = x[0] + (0.49 - x[0])*exp_term if needfi == fi + 1: return f if mode in [1, 2]: fjsl[fi, 0] = 1. - exp_term fjsl[fi, 1] = -(0.49 - x[0])*(a[fi] - 8.)*exp_term return f def cb_start(quas, repeat1, bl, bu): "Function to set up the starting points for the optimization." quas[:, :] = [ [0.4, 0., 0.], [0., 1., 0.], ] # Initialize the communication structure for the solver: comm = {} glopt.optset('Initialize = nlp_multistart_sqp_lsq', comm) # nlp_multistart_sqp_lsq may trigger a 'Warning' when a # start-point failed to produce a convergent solution. # By promoting this warning to an error and catching the specific # exit case (errno 8) we can determine the number of # converged solutions if this happens, from the 'info' # return data. warnings.simplefilter('error', utils.NagAlgorithmicWarning) try: objf = glopt.nlp_multistart_sqp_lsq( ncnln, bl, bu, y, cb_objfun, npts, nb, comm, a=a, confun=cb_confun, start=cb_start, repeat1=True, ).objf n_sol = nb except utils.NagAlgorithmicWarning as exc: if exc.errno == 8: objf = exc.return_data.objf n_sol = exc.return_data.info[nb-1] else: raise exc for sol_i in range(n_sol): print('Solution number {:d}.'.format(sol_i + 1)) print('Final objective value = {:15.7f}.'.format(objf[sol_i]))
if __name__ == '__main__': import doctest import sys sys.exit( doctest.testmod( None, verbose=True, report=False, optionflags=doctest.REPORT_NDIFF, ).failed )