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Nonlinear Programming and Variational Inequality Problems - A Unified Approach (Hardcover, 1999 ed.)
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Nonlinear Programming and Variational Inequality Problems - A Unified Approach (Hardcover, 1999 ed.)
Series: Applied Optimization, 23
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Since I started working in the area of nonlinear programming and,
later on, variational inequality problems, I have frequently been
surprised to find that many algorithms, however scattered in
numerous journals, monographs and books, and described rather
differently, are closely related to each other. This book is meant
to help the reader understand and relate algorithms to each other
in some intuitive fashion, and represents, in this respect, a
consolidation of the field. The framework of algorithms presented
in this book is called Cost Approxi mation. (The preface of the
Ph.D. thesis Pat93d] explains the background to the work that lead
to the thesis, and ultimately to this book.) It describes, for a
given formulation of a variational inequality or nonlinear
programming problem, an algorithm by means of approximating
mappings and problems, a principle for the update of the iteration
points, and a merit function which guides and monitors the
convergence of the algorithm. One purpose of this book is to offer
this framework as an intuitively appeal ing tool for describing an
algorithm. One of the advantages of the framework, or any
reasonable framework for that matter, is that two algorithms may be
easily related and compared through its use. This framework is
particular in that it covers a vast number of methods, while still
being fairly detailed; the level of abstraction is in fact the same
as that of the original problem statement."
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