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The aim here is to become familiar with the broad range of
optimization software now available.  Most packages are licensed,
but there are open source solvers in some categories, and
NEOS is freely accessible.

There are two main solution methods for continuous optimization.

\emph{Active-set methods} tend to need many ``cheap'' iterations
(because certain sparse-matrix factorizations can be updated).
They can be restarted easily if the problem is modified.

\emph{Interior methods} (also called \emph{interior-point methods})
need relatively few iterations involving more expensive linear
algebra.  So far, there is little progress toward warm-starting them.

\medskip

\begin{enumerate}

\item
  Review the GAMS website: \url{http://www.gams.com}.
  \begin{enumerate}
  \item Try to find all the solvers that can solve LP problems.
    (This may include nonlinear solvers.)

  \item Find the solvers that can handle general NLP problems
    (with nonlinear objective and/or nonlinear constraints).

  \item Is there a solver that can solve LP and QP problems
    but not general NLPs?
  \end{enumerate}

\item
  Review the AMPL website: \url{http://www.ampl.com}.
  \begin{enumerate}
  \item Find the solvers that can solve MILP problems
    (linear programs with some integer variables).

  \item Find as many solvers as you can that solve general NLP problems
    using an \emph{interior method}.
  \end{enumerate}
  
\item Review the NEOS Server for Optimization:
  \url{http://www-neos.mcs.anl.gov}.  In particular, study the FAQ page.
  \begin{enumerate}
  \item For an LP model, is it easy or hard to determine
        if a feasible solution exists (compared to finding an
        optimal solution)?
  \item In the context of LP and NLP, what does ``Programming''
        really mean?
  \end{enumerate}

\item If you need to solve some optimization problems
  from within \Matlab, which systems could you consider?
  (One or two will do.)

\end{enumerate}

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