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Books > Science & Mathematics > Mathematics > Optimization
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Sparse Polynomial Optimization: Theory And Practice (Hardcover)
Loot Price: R2,346
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Sparse Polynomial Optimization: Theory And Practice (Hardcover)
Series: Series On Optimization And Its Applications, 5
Expected to ship within 10 - 15 working days
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Many applications, including computer vision, computer arithmetic,
deep learning, entanglement in quantum information, graph theory
and energy networks, can be successfully tackled within the
framework of polynomial optimization, an emerging field with
growing research efforts in the last two decades. One key advantage
of these techniques is their ability to model a wide range of
problems using optimization formulations. Polynomial optimization
heavily relies on the moment-sums of squares (moment-SOS) approach
proposed by Lasserre, which provides certificates for positive
polynomials. On the practical side, however, there is 'no free
lunch' and such optimization methods usually encompass severe
scalability issues. Fortunately, for many applications, including
the ones formerly mentioned, we can look at the problem in the eyes
and exploit the inherent data structure arising from the cost and
constraints describing the problem.This book presents several
research efforts to resolve this scientific challenge with
important computational implications. It provides the development
of alternative optimization schemes that scale well in terms of
computational complexity, at least in some identified class of
problems. It also features a unified modeling framework to handle a
wide range of applications involving both commutative and
noncommutative variables, and to solve concretely large-scale
instances. Readers will find a practical section dedicated to the
use of available open-source software libraries.This
interdisciplinary monograph is essential reading for students,
researchers and professionals interested in solving optimization
problems with polynomial input data.
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