lines 6-59 of file: example/python/numeric/optimize_fun_xam.py

# {xrst_begin numeric_optimize_fun_xam.py}
# {xrst_spell
#     constr
#     cr
#     ipopt
#     scipy
# }
# {xrst_comment_ch #}
#
#
# Example Using optimize_fun_class with Scipy Optimization
# ########################################################
#
# Reference
# *********
# This problem comes form the
# `Interfaces <https://coin-or.github.io/Ipopt/INTERFACES.html>`_
# section of the Ipopt documentation.
#
# Problem
# *******
#
# .. math::
#
#    \begin{array}{cr}
#    {\rm minimize}      & x_0 x_3 ( x_0 + x_1 + x_2 ) + x_2   \\
#    {\rm subject \; to} &             x_0 x_1 x_2 x_3 \geq 25 \\
#                         & x_0^2 + x_1^2 + x_2^2 + x_3^2 = 40  \\
#                         &                    1 \leq x \leq 5
#    \end{array}
#
# with the starting point :math:`x = (1, 5, 5, 1)`.
# The optimal value for :math:`x` is
#
# .. math::
#
#  \newcommand{\W}[1]{{\; #1 \;}}
#  (1.00000000 \W{,} 4.74299963 \W{,} 3.82114998 \W{,} 1.37940829)
#
# trust_constr
# ************
# This is one of the
# `scipy.optimize
# <https://docs.scipy.org/doc/scipy/reference/optimize.html>`_
# methods.
#
# Source Code
# ***********
# {xrst_literal
#  # BEGIN_PYTHON
#  # END_PYTHON
# }
#
# {xrst_end numeric_optimize_fun_xam.py}