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Everything should be made as simple as possible, but not simpler.
(Albert Einstein, Readers Digest, 1977) The modern practice of
creating technical systems and technological processes of high
effi.ciency besides the employment of new principles, new
materials, new physical effects and other new solutions ( which is
very traditional and plays the key role in the selection of the
general structure of the object to be designed) also includes the
choice of the best combination for the set of parameters
(geometrical sizes, electrical and strength characteristics, etc.)
concretizing this general structure, because the Variation of these
parameters ( with the structure or linkage being already set
defined) can essentially affect the objective performance indexes.
The mathematical tools for choosing these best combinations are
exactly what is this book about. With the advent of computers and
the computer-aided design the pro bations of the selected variants
are usually performed not for the real examples ( this may require
some very expensive building of sample op tions and of the special
installations to test them ), but by the analysis of the
corresponding mathematical models. The sophistication of the
mathematical models for the objects to be designed, which is the
natu ral consequence of the raising complexity of these objects,
greatly com plicates the objective performance analysis. Today, the
main (and very often the only) available instrument for such an
analysis is computer aided simulation of an object's behavior,
based on numerical experiments with its mathematical model.
Everything should be made as simple as possible, but not simpler.
(Albert Einstein, Readers Digest, 1977) The modern practice of
creating technical systems and technological processes of high
effi.ciency besides the employment of new principles, new
materials, new physical effects and other new solutions ( which is
very traditional and plays the key role in the selection of the
general structure of the object to be designed) also includes the
choice of the best combination for the set of parameters
(geometrical sizes, electrical and strength characteristics, etc.)
concretizing this general structure, because the Variation of these
parameters ( with the structure or linkage being already set
defined) can essentially affect the objective performance indexes.
The mathematical tools for choosing these best combinations are
exactly what is this book about. With the advent of computers and
the computer-aided design the pro bations of the selected variants
are usually performed not for the real examples ( this may require
some very expensive building of sample op tions and of the special
installations to test them ), but by the analysis of the
corresponding mathematical models. The sophistication of the
mathematical models for the objects to be designed, which is the
natu ral consequence of the raising complexity of these objects,
greatly com plicates the objective performance analysis. Today, the
main (and very often the only) available instrument for such an
analysis is computer aided simulation of an object's behavior,
based on numerical experiments with its mathematical model."
Introduction to Global Optimization Exploiting Space-Filling Curves
provides an overview of classical and new results pertaining to the
usage of space-filling curves in global optimization. The authors
look at a family of derivative-free numerical algorithms applying
space-filling curves to reduce the dimensionality of the global
optimization problem; along with a number of unconventional ideas,
such as adaptive strategies for estimating Lipschitz constant,
balancing global and local information to accelerate the search.
Convergence conditions of the described algorithms are studied in
depth and theoretical considerations are illustrated through
numerical examples. This work also contains a code for implementing
space-filling curves that can be used for constructing new global
optimization algorithms. Basic ideas from this text can be applied
to a number of problems including problems with multiextremal and
partially defined constraints and non-redundant parallel
computations can be organized. Professors, students, researchers,
engineers, and other professionals in the fields of pure
mathematics, nonlinear sciences studying fractals, operations
research, management science, industrial and applied mathematics,
computer science, engineering, economics, and the environmental
sciences will find this title useful .
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