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Convex Analysis and Global Optimization (Paperback, Softcover reprint of hardcover 1st ed. 1998)
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Convex Analysis and Global Optimization (Paperback, Softcover reprint of hardcover 1st ed. 1998)
Series: Nonconvex Optimization and Its Applications, 22
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Due to the general complementary convex structure underlying most
nonconvex optimization problems encountered in applications, convex
analysis plays an essential role in the development of global
optimization methods. This book develops a coherent and rigorous
theory of deterministic global optimization from this point of
view. Part I constitutes an introduction to convex analysis, with
an emphasis on concepts, properties and results particularly needed
for global optimization, including those pertaining to the
complementary convex structure. Part II presents the foundation and
application of global search principles such as partitioning and
cutting, outer and inner approximation, and decomposition to
general global optimization problems and to problems with a
low-rank nonconvex structure as well as quadratic problems. Much
new material is offered, aside from a rigorous mathematical
development. Audience: The book is written as a text for graduate
students in engineering, mathematics, operations research, computer
science and other disciplines dealing with optimization theory. It
is also addressed to all scientists in various fields who are
interested in mathematical optimization.
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