The theory of optimization, understood in a broad sense, is the
basis of modern applied mathematics, covering a large spectrum of
topics from theoretical considerations (structure, stability) to
applied operational research and engineering applications. The
compiled material of this book puts on display this versatility, by
exhibiting the three parallel and complementary components of
optimization: theory, algorithms, and practical problems.
The book contains an expanded version of three series of
lectures delivered by the authors at the CRM in July 2009. The
first part is a self-contained course on the general moment problem
and its relations with semidefinite programming. The second part is
dedicated to the problem of determination of Nash equilibria from
an algorithmic viewpoint. The last part presents congestion models
for traffic networks and develops modern optimization techniques
for finding traffic equilibria based on stochastic optimization and
game theory.
General
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