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Introductory Lectures on Convex Optimization - A Basic Course (Hardcover, 2004 ed.)
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Introductory Lectures on Convex Optimization - A Basic Course (Hardcover, 2004 ed.)
Series: Applied Optimization, 87
Expected to ship within 10 - 15 working days
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It was in the middle of the 1980s, when the seminal paper by Kar
markar opened a new epoch in nonlinear optimization. The importance
of this paper, containing a new polynomial-time algorithm for
linear op timization problems, was not only in its complexity
bound. At that time, the most surprising feature of this algorithm
was that the theoretical pre diction of its high efficiency was
supported by excellent computational results. This unusual fact
dramatically changed the style and direc tions of the research in
nonlinear optimization. Thereafter it became more and more common
that the new methods were provided with a complexity analysis,
which was considered a better justification of their efficiency
than computational experiments. In a new rapidly develop ing field,
which got the name "polynomial-time interior-point methods", such a
justification was obligatory. Afteralmost fifteen years of
intensive research, the main results of this development started to
appear in monographs [12, 14, 16, 17, 18, 19]. Approximately at
that time the author was asked to prepare a new course on nonlinear
optimization for graduate students. The idea was to create a course
which would reflect the new developments in the field. Actually,
this was a major challenge. At the time only the theory of
interior-point methods for linear optimization was polished enough
to be explained to students. The general theory of self-concordant
functions had appeared in print only once in the form of research
monograph [12].
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