03223nam 2200529Ia 450 991073947530332120200520144314.01-4614-8042-610.1007/978-1-4614-8042-6(OCoLC)857280006(MiFhGG)GVRL6YBL(CKB)3710000000015783(MiAaPQ)EBC1398506(EXLCZ)99371000000001578320111102d2013 uy 0engurun|---uuuuatxtccrIntroduction to global optimization exploiting space-filling curves /Yaroslav D. Sergeyev, Roman G. Strongin, Daniela Lera1st ed. 2013.New York Springer20131 online resource (x, 125 pages) illustrations (some color)SpringerBriefs in optimization"ISSN: 2190-8354.""ISSN: 2191-575X (electronic)."1-4614-8041-8 Includes bibliographical references.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 . .SpringerBriefs in optimization.CurvesMathematical modelsCurves on surfacesMathematical modelsCurvesMathematical models.Curves on surfacesMathematical models.519.6Sergeyev Yaroslav D.1963-1755455Strongin Roman G724333Lera Daniela1755456MiAaPQMiAaPQMiAaPQBOOK9910739475303321Introduction to global optimization exploiting space-filling curves4192236UNINA