Harvard Applied Math 205: Code Examples
Unit 4: Nonlinear Equations and Optimization
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bisection.py - Demonstrates the one-dimensional bisection root-finding
algorithm.

iter.py - Demonstrates two possible fixed-point iterations for finding the
solution to a nonlinear equation. One converges to the solution, whereas the
other diverges.

iter_2d.py - Demonstrates a fixed-point iteration to find the solution of a
two-dimensional nonlinear function.

gq_solve.py - Compares a custom implementation of the Newton method to
Python's "fsolve" routine for finding the nodes and weights in the two-point
Gauss quadrature scheme.

n_secant.py - Uses the Newton and secant methods to find the solution to a
nonlinear equation.

himmelblau.py - A common program file that defines the Himmelblau function, a
common optimization benchmark function. The Jacobian and Hessian of the
Himmelblau function are also defined. This file is used by the h_sdescent.py,
h_newton.py, and h_bfgs.py examples.

h_sdescent.py - Finds minima of the Himmelblau function using the steepest
descent method.

h_newton.py - Finds critical points of the Himmelblau function using the
Newton method.

h_bfgs.py - Finds minima of the Himmelblau function using the BFGS
optimization method.

penalty.py - Demonstrates solving a constrained optimization problem using
the penalty method.

linprog.py - this Python program solves the linear program described in the
slides. It makes use of the Python module cvxopt that is available online.

linprog_alt.py - this is an alternative Python program that solves the same
linear program, but with the linprog library in SciPy.

feasible.gnu - Data to draw the wireframe outline of the feasible set for
the example linear program. In Gnuplot, type "splot 'feasible.gnu' with lp"
to see a 3D plot of the outline.