  The field of optimization has gotten a lot of interest in recent years owing
to significant advances in computer technology. Numerous issues in machine
learning, economics, finance, geophysics, molecular modeling, computational
systems biology, operations research, and all areas of engineering are now
being resolved owing to the rapid growth of optimization methods and
algorithms. This monograph presents the main theorems in linear algebra, convex
sets, convex functions, single variable optimization, multivariable
optimization, and their corresponding algorithms. We also briefly touch upon
the constrained nonlinear optimization. We have found the Wolfram language to
be ideal for specifying algorithms in human readable form. To minimize
nonlinear objective functions, we have created 27 Mathematica functions that
follow the principles of 18 algorithms. The code examples were carefully
designed to demonstrate the purpose of given algorithm. The code for each
algorithm will run as is with no code from prior algorithms or third parties
required beyond the installation of Mathematica.
