Introduction to Global Optimization Exploiting Space-Filling Curves
Springer Science & Business Media, Aug 13, 2013 - Mathematics - 125 pages
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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100 functions acceleration adaptive estimate adjacent subcubes approximation calculated centers yi ci(x computing consider constructed convergence coordinate corresponding cube D(zi denoted dimension evolvent follows FORTRAN function evaluations function f(x geometric global minimizer global optimization algorithms global optimization problems global search grid H¨older constant hypercube imin improvement technique indexes z1 Information Algorithm integer interval x_1,x interval xi−1,xi introduced inverse images juxtaposed LBDirect limit point linear Lipschitz condition Lipschitz constant Lipschitz global optimization Lipschitzian LTLI mapping MILI minimum Mth partition multiextremal nodes number of function number of trials numerical experiments objective function obtained one-dimensional Peano curve piecewise-linear Piyavskii point xk+1 preimage printf reliability parameter satisfies scheme GS search region Sect sequence xk Sergeyev series of experiments solving space-filling curves Step stopping rule Strongin Table test class test functions Theorem trial points tuning unit interval utq(s vector w(zi Ya.D