Introduction to Global Optimization Exploiting Space-Filling Curves

"Introduction to Global Optimization Exploiting Space-Filling Curves" provides a comprehensive overview of classical and new results regarding the application of Space-Filling Curves in global optimization. The authors present a series of derivative-free numerical algorithms that utilize Space-Filling Curves to reduce the dimensionality of global optimization problems. Additionally, unconventional approaches such as adaptive strategies for estimating Lipschitz constants and balancing global and local information to accelerate the search are explored. The convergence conditions of the described algorithms are analyzed in detail, and theoretical considerations are illustrated through numerical examples. The work also includes code for implementing Space-Filling Curves, which can be used to develop new global optimization algorithms. The fundamental ideas of this text are applicable to a variety of problems, including those with multi-extremal and partially defined constraints, as well as the organization of non-redundant parallel computations. This book is aimed at professors, students, researchers, engineers, and other professionals in the fields of pure mathematics, nonlinear sciences, operations research, management sciences, industrial and applied mathematics, computer science, economics, and environmental sciences.