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This eBook is a collection of articles from a Frontiers Research Topic. Frontiers Research Topics are very popular trademarks of the Frontiers Journals Series: they are collections of at least ten articles, all centered on a particular subject. With their unique mix of varied contributions from Original Research to Review Articles, Frontiers Research Topics unify the most influential researchers, the latest key findings and historical advances in a hot research area! Find out more on how to host your own Frontiers Research Topic or contribute to one as an author by contacting the Frontiers Editorial Office: frontiersin.org/about/contact

molecular geometry search --- fitting potential energy functions --- spectral assignment --- global optimization algorithms --- energy landscapes

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Simplicial Global Optimization is centered on deterministic covering methods partitioning feasible region by simplices. This book looks into the advantages of simplicial partitioning in global optimization through applications where the search space may be significantly reduced while taking into account symmetries of the objective function by setting linear inequality constraints that are managed by initial partitioning. The authors provide an extensive experimental investigation and illustrates the impact of various bounds, types of subdivision, strategies of candidate selection on the performance of algorithms. A comparison of various Lipschitz bounds over simplices and an extension of Lipschitz global optimization with-out the Lipschitz constant to the case of simplicial partitioning is also depicted in this text. Applications benefiting from simplicial partitioning are examined in detail such as nonlinear least squares regression and pile placement optimization in grillage-type foundations. Researchers and engineers will benefit from simplicial partitioning algorithms such as Lipschitz branch and bound, Lipschitz optimization without the Lipschitz constant, heuristic partitioning presented. This book will leave readers inspired to develop simplicial versions of other algorithms for global optimization and even use other non-rectangular partitions for special applications.

Mathematics. --- Combinatorial analysis. --- Nonconvex programming. --- Global optimization --- Non-convex programming --- Combinatorics --- Math --- Applied mathematics. --- Engineering mathematics. --- Operations research. --- Management science. --- Combinatorics. --- Operations Research, Management Science. --- Applications of Mathematics. --- Programming (Mathematics) --- Algebra --- Mathematical analysis --- Science --- Engineering --- Engineering analysis --- Quantitative business analysis --- Management --- Problem solving --- Operations research --- Statistical decision --- Operational analysis --- Operational research --- Industrial engineering --- Management science --- Research --- System theory --- Mathematics --- Mathematical optimization.

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This book is focused on fractional order systems. Historically, fractional calculus has been recognized since the inception of regular calculus, with the first written reference dated in September 1695 in a letter from Leibniz to L’Hospital. Nowadays, fractional calculus has a wide area of applications in areas such as physics, chemistry, bioengineering, chaos theory, control systems engineering, and many others. In all those applications, we deal with fractional order systems in general. Moreover, fractional calculus plays an important role even in complex systems and therefore allows us to develop better descriptions of real-world phenomena. On that basis, fractional order systems are ubiquitous, as the whole real world around us is fractional. Due to this reason, it is urgent to consider almost all systems as fractional order systems.

complexity --- cuckoo search --- magnetic resonance imaging --- fractional calculus --- musical signal --- pinning synchronization --- Fourier transform --- optimal randomness --- fractional-order system --- Mittag-Leffler function --- meaning --- parameter --- diffusion-wave equation --- anomalous diffusion --- Laplace transform --- time-varying delays --- mass absorption --- swarm-based search --- fractional --- adaptive control --- time series --- Hurst exponent --- fractional derivative --- control --- PID --- global optimization --- reaction–diffusion terms --- audio signal processing --- Caputo derivative --- harmonic impact --- fractional complex networks --- heavy-tailed distribution --- impulses --- long memory --- linear prediction

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The articles that comprise this distinguished annual volume for the Advances in Mechanics and Mathematics series have been written in honor of Gilbert Strang, a world renowned mathematician and exceptional person. Written by leading experts in complementarity, duality, global optimization, and quantum computations, this collection reveals the beauty of these mathematical disciplines and investigates recent developments in global optimization, nonconvex and nonsmooth analysis, nonlinear programming, theoretical and engineering mechanics, large scale computation, quantum algorithms and computation, and information theory. Much of the material, including the various methodologies, is written for nonexperts and is intended to stimulate graduate students and young faculty to venture into this rich domain of research; it will also benefit researchers and practitioners in several areas of applied mathematics, mechanics, and engineering.

Mathematical optimization --Congresses. --- Mechanics --Congresses. --- Mechanics --Mathematics --Congresses. --- Mechanics --- Mathematical optimization --- Engineering & Applied Sciences --- Applied Mathematics --- Mathematics --- Statistical mechanics --- Classical mechanics --- Newtonian mechanics --- Mathematics. --- Computer mathematics. --- Computer software. --- Calculus of variations. --- Mechanical engineering. --- Calculus of Variations and Optimal Control; Optimization. --- Mechanical Engineering. --- Computational Mathematics and Numerical Analysis. --- Mathematical Software. --- Engineering, Mechanical --- Engineering --- Machinery --- Steam engineering --- Isoperimetrical problems --- Variations, Calculus of --- Maxima and minima --- Software, Computer --- Computer systems --- Computer mathematics --- Discrete mathematics --- Electronic data processing --- Math --- Science --- Physics --- Dynamics --- Quantum theory --- Mathematical optimization. --- Computer science --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Operations research --- Simulation methods --- System analysis --- Applied mathematics --- Global optimization --- Complementarity --- Duality

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Aerodynamic design, like many other engineering applications, is increasingly relying on computational power. The growing need for multi-disciplinarity and high fidelity in design optimization for industrial applications requires a huge number of repeated simulations in order to find an optimal design candidate. The main drawback is that each simulation can be computationally expensive – this becomes an even bigger issue when used within parametric studies, automated search or optimization loops, which typically may require thousands of analysis evaluations. The core issue of a design-optimization problem is the search process involved. However, when facing complex problems, the high-dimensionality of the design space and the high-multi-modality of the target functions cannot be tackled with standard techniques. In recent years, global optimization using meta-models has been widely applied to design exploration in order to rapidly investigate the design space and find sub-optimal solutions. Indeed, surrogate and reduced-order models can provide a valuable alternative at a much lower computational cost. In this context, this volume offers advanced surrogate modeling applications and optimization techniques featuring reasonable computational resources. It also discusses basic theory concepts and their application to aerodynamic design cases. It is aimed at researchers and engineers who deal with complex aerodynamic design problems on a daily basis and employ expensive simulations to solve them.

Aeronautics Engineering & Astronautics --- Mechanical Engineering --- Engineering & Applied Sciences --- Aerodynamics --- Nonconvex programming. --- Mathematical models. --- Computer simulation. --- Global optimization --- Non-convex programming --- Aerodynamics, Subsonic --- Airplanes --- Streamlining --- Subsonic aerodynamics --- Programming (Mathematics) --- Dynamics --- Fluid dynamics --- Gas dynamics --- Pneumatics --- Aeronautics --- Wind tunnels --- Astronautics. --- Hydraulic engineering. --- Engineering design. --- Aerospace Technology and Astronautics. --- Engineering Fluid Dynamics. --- Engineering Design. --- Simulation and Modeling. --- Computer modeling --- Computer models --- Modeling, Computer --- Models, Computer --- Simulation, Computer --- Electromechanical analogies --- Mathematical models --- Simulation methods --- Model-integrated computing --- Design, Engineering --- Engineering --- Industrial design --- Strains and stresses --- Engineering, Hydraulic --- Fluid mechanics --- Hydraulics --- Shore protection --- Space sciences --- Astrodynamics --- Space flight --- Space vehicles --- Design --- Aerospace engineering. --- Fluid mechanics. --- Hydromechanics --- Continuum mechanics --- Aeronautical engineering --- Astronautics