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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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