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{\bf SEMIDEFINITE PROGRAMMING AND ITS APPLICATIONS\\
Prof. Henry Wolkowicz\\
Dept. Comb. \& Opt.,
Univ. of Waterloo, Fall 1998
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Semidefinite programming
(SDP)  refers to mathematical programs of the type
\[ \min f(x) \mbox{ subject to } g(x) \preceq 0, x \in \Omega, \]
where $f,g$ are matrix valued functions and $A \preceq B$ refers to the 
L{\"{o}}wner partial order, i.e. the symmetric matrix $B-A$ is positive
semidefinite.

Though these problems have been studied before, it is only recently that
the combination of important applications with implementable algorithms
has resulted in intensive research activity. This area is proving to be
of major importance because of the many applications; in addition, the
high mathematical elegance is attracting many researchers.

This course will provide a thorough treatment of semidefinite
programming.
\begin{enumerate}
\item
THEORY
\begin{enumerate}
\item
Convex analysis on symmetric matrices
\item
Geometry of SDP
\item
First and second order optimality conditions; duality
\item
Error analysis and parametric programming
\end{enumerate}
\item
ALGORITHMS
\begin{enumerate}
\item
Potential reduction methods
\item
path-following methods
\item
implementation
\end{enumerate}
\item
APPLICATIONS
\begin{enumerate}
\item
Combinatorial Optimization problems (e.g.
quadratic assignment, graph partitioning, max-cut, general integer)
\item
eigenvalue optimization
\item
matrix completion problems
\item
nonconvex quadratic optimization
\end{enumerate}
\end{enumerate}
Possible additional speakers: Romesh Saigal, Univ.
of Michigan; Tom Luo and Jose Sturm, McMaster Univ.; Lieven
Vandenberghe, UCLA; Gabor Pataki, DIMACS.\\
Tentative Time:  Tuesday and Thursday 1-2:30 PM.

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