04272nam a22006255i 4500 978-1-4614-8042-6 DE-He213 20210617034113.0 cr nn 008mamaa 130805s2013 xxu| s |||| 0|eng d 9781461480426 978-1-4614-8042-6 10.1007/978-1-4614-8042-6 doi QA613-613.8 QA613.6-613.66 PBMS bicssc MAT038000 bisacsh PBMS thema PBPH thema 514.34 23 Sergeyev, Yaroslav D. author. aut http://id.loc.gov/vocabulary/relators/aut Introduction to Global Optimization Exploiting Space-Filling Curves [electronic resource] / by Yaroslav D. Sergeyev, Roman G. Strongin, Daniela Lera. 1st ed. 2013. New York, NY : Springer New York : Imprint: Springer, 2013. X, 125 p. 32 illus., 30 illus. in color. online resource. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda SpringerBriefs in Optimization, 2190-8354 1. Introduction -- 2. Approximations to Peano curves -- 3. Global optimization algorithms using curves to reduce dimensionality of the problem -- 4. Ideas for acceleration -- 5. A brief conclusion -- References. 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 . . Manifolds (Mathematics). Complex manifolds. Operations research. Management science. Computer software. Numerical analysis. Algebraic geometry. Manifolds and Cell Complexes (incl. Diff.Topology). https://scigraph.springernature.com/ontologies/product-market-codes/M28027 Operations Research, Management Science. https://scigraph.springernature.com/ontologies/product-market-codes/M26024 Mathematical Software. https://scigraph.springernature.com/ontologies/product-market-codes/M14042 Numerical Analysis. https://scigraph.springernature.com/ontologies/product-market-codes/M14050 Algebraic Geometry. https://scigraph.springernature.com/ontologies/product-market-codes/M11019 Strongin, Roman G. author. aut http://id.loc.gov/vocabulary/relators/aut Lera, Daniela. author. aut http://id.loc.gov/vocabulary/relators/aut SpringerLink (Online service) Springer Nature eBook Printed edition: 9781461480433 Printed edition: 9781461480419 SpringerBriefs in Optimization, 2190-8354 https://doi.org/10.1007/978-1-4614-8042-6 ZDB-2-SMA ZDB-2-SXMS Mathematics and Statistics (SpringerNature-11649) Mathematics and Statistics (R0) (SpringerNature-43713)