Introduction to Global Optimization Exploiting Space-Filling Curves
Introduction to Global Optimization Exploiting Space-Filling Curves
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DOI：
10.1007/978-1-4614-8042-6
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发表时间：
2013-07
期刊：
影响因子：
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通讯作者：
Y. Sergeyev;R. Strongin;D. Lera
中科院分区：
文献类型：
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作者：
Y. Sergeyev;R. Strongin;D. Lera
利用空间填充曲线的全局优化概论提供了关于在全局优化中使用空间填充曲线的经典和新结果的概述。作者研究了一组应用空间填充曲线来降低全局优化问题维数的无导数数值算法；还有一些非常规的想法，比如估算Lipschitz常数的自适应策略，平衡全局和局部信息以加速搜索。深入研究了所述算法的收敛条件，并通过数值算例说明了理论考虑。这项工作还包含实现空间填充曲线的代码，该曲线可用于构建新的全局优化算法。本文的基本思想可以应用于许多问题，包括具有多极值和部分定义约束的问题以及可以组织的非冗余并行计算。纯数学、研究分形的非线性科学、运筹学、管理科学、工业和应用数学、计算机科学、工程学、经济学和环境科学等领域的教授、学生、研究人员、工程师和其他专业人士都会发现这本书很有用。
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.