\documentstyle[11pt]{article}
\begin{document}

\begin{center}
{\large\bf  Proposed New C\&O Comprehensive Exam Syllabus for \\ 
    Continuous Optimization\\
}
\end{center}

\begin{description}
  \item[  Examiners:]~~~
              TBA
 
  \item[  References:]~~~  
%Except for complexity,
%the  material is covered (with some overlap) in the books:
\begin{enumerate}
\item
 Convex Optimization S. Boyd and L. Vandenberghe, [QA402.5.B69 2004]
\item
Fundamentals of Convex Analysis, 
J.-B. Hiriart-Urruty and C. Lemaréchal, 
Springer, 2001
\item
 Convex Analysis and Nonlinear Optimization, J.M Borwein and A. Lewis, [QA331.5.B65 2006]
\item
Convex Analysis and Optimization,
Dimitri P. Bertsekas
(with Angelia Nedic and Asuman E. Ozdaglar)
\item
 Convex Analysis, R.T. Rockafellar, [QA300.R573]
\item
 Lectures on modern convex optimization : analysis, algorithms, and engineering applica-
tions, A. Ben-Tal and A. Nemirovski, [T57.815.B46]
\item
The Mathematics of
Nonlinear Programming, Peressini, Sullivan, Uhl


\end{enumerate}

  \item[  Outline:]~~~ 
\begin{enumerate}
\item
Some canonical forms of convex optimization problems.
\item
basic unconstrained optimization? basic linear programming?
\item
Convex Sets:
structure of convex sets, convex hulls, separation of convex sets, 
support functions, supporting hyperplanes, tangent and normal cones, 
some theory of convex geometry.
\item
Convex Functions:
differentiability and subgradient calculus, 
Fenchel-Legendre conjugates and duality,
sublinear functions and norms
\item
Lagrange multipliers, Lagrangian duality, KKT optimality conditions, 
minmax theory.
\item
Numerical methods for convex optimization.
\item
Ellipsoid Method and computational complexity of convex optimization,
The classes P and NP, NP-completeness. Reference: Combinatorial
Optimization,
Cook-Cunningham-Pulleyblank-Schrijver, pages 309-323.
\end{enumerate}

\end{description}
\end{document}
