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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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In the field of nondifferentiable nonconvex optimization, one of the most intensely investigated areas is that of optimization problems involving multivalued mappings in constraints or as the objective function. This book focuses on the tremendous development in the field that has taken place since the publication of the most recent volumes on the subject. The new topics studied include the formulation of optimality conditions using different kinds of generalized derivatives for set-valued mappings (such as, for example, the coderivative of Mordukhovich), the opening of new applications (e.g., the calibration of water supply systems), or the elaboration of new solution algorithms (e.g., smoothing methods). The book is divided into three parts. The focus in the first part is on bilevel programming. The chapters in the second part contain investigations of mathematical programs with equilibrium constraints. The third part is on multivalued set-valued optimization. The chapters were written by outstanding experts in the areas of bilevel programming, mathematical programs with equilibrium (or complementarity) constraints (MPEC), and set-valued optimization problems. Audience This book is intended for researchers, graduate students and practitioners in the fields of applied mathematics, operations research, and economics.

Nonlinear programming. --- Nonconvex programming. --- Set-valued maps. --- Game theory. --- Games, Theory of --- Theory of games --- Mathematical models --- Mathematics --- Many-valued mappings --- Mappings, Point-to-set --- Maps, Set-valued --- Multi-valued mappings --- Multivalued mappings --- Point-to-set mappings --- Mappings (Mathematics) --- Selection theorems --- Global optimization --- Non-convex programming --- Programming (Mathematics) --- Mathematical optimization. --- Optimization. --- Calculus of Variations and Optimal Control; Optimization. --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Calculus of variations. --- Isoperimetrical problems --- Variations, Calculus of

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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

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Recent developments in theory, algorithms, and applications in optimization and control are discussed in this proceedings, based on selected talks from the ‘Optimization, Control, and Applications in the Information Age’ conference, organized in honor of Panos Pardalos’s 60th birthday. This volume contains numerous applications to optimal decision making in energy production and fuel management, data mining, logistics, supply chain management, market network analysis, risk analysis, and community network analysis.  In addition, a short biography is included describing Dr. Pardalos’s path from a shepherd village on the high mountains of Thessaly to academic success. Due to the wide range of topics such as global optimization, combinatorial optimization, game theory, stochastics and programming contained in this publication, scientists, researchers, and students in optimization, operations research, analytics, mathematics and computer science will be interested in this volume.

Mathematics. --- Calculus of Variations and Optimal Control; Optimization. --- Game Theory/Mathematical Methods. --- Mathematical Modeling and Industrial Mathematics. --- Probability Theory and Stochastic Processes. --- Mathematical optimization. --- Distribution (Probability theory). --- Economics, Mathematical. --- Mathématiques --- Optimisation mathématique --- Distribution (Théorie des probabilités) --- Mathématiques économiques --- Nonconvex programming. --- Civil & Environmental Engineering --- Mathematics --- Engineering & Applied Sciences --- Physical Sciences & Mathematics --- Operations Research --- Calculus --- Global optimization --- Non-convex programming --- Operations research. --- Decision making. --- Mathematical models. --- Calculus of variations. --- Probabilities. --- Operation Research/Decision Theory. --- Programming (Mathematics) --- Distribution (Probability theory. --- Operations Research/Decision Theory. --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Operational analysis --- Operational research --- Industrial engineering --- Management science --- Research --- System theory --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Probability --- Statistical inference --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk --- Models, Mathematical --- Deciding --- Decision (Psychology) --- Decision analysis --- Decision processes --- Making decisions --- Management --- Management decisions --- Choice (Psychology) --- Problem solving --- Isoperimetrical problems --- Variations, Calculus of --- Decision making

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Accessible to a variety of readers, this book is of interest to specialists, graduate students and researchers in mathematics, optimization, computer science, operations research, management science, engineering and other applied areas interested in solving optimization problems. Basic principles, potential and boundaries of applicability of stochastic global optimization techniques are examined in this book. A variety of issues that face specialists in global optimization are explored, such as multidimensional spaces which are frequently ignored by researchers. The importance of precise interpretation of the mathematical results in assessments of optimization methods is demonstrated through examples of convergence in probability of random search. Methodological issues concerning construction and applicability of stochastic global optimization methods are discussed, including the one-step optimal average improvement method based on a statistical model of the objective function. A significant portion of this book is devoted to an analysis of high-dimensional global optimization problems and the so-called ‘curse of dimensionality’. An examination of the three different classes of high-dimensional optimization problems, the geometry of high-dimensional balls and cubes, very slow convergence of global random search algorithms in large-dimensional problems , and poor uniformity of the uniformly distributed sequences of points are included in this book. .

Calculus of variations. --- Industrial engineering. --- Production engineering. --- Probabilities. --- Matrix theory. --- Algebra. --- Calculus of Variations and Optimal Control; Optimization. --- Industrial and Production Engineering. --- Probability Theory and Stochastic Processes. --- Linear and Multilinear Algebras, Matrix Theory. --- Mathematics --- Mathematical analysis --- Probability --- Statistical inference --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk --- Manufacturing engineering --- Process engineering --- Industrial engineering --- Mechanical engineering --- Management engineering --- Simplification in industry --- Engineering --- Value analysis (Cost control) --- Isoperimetrical problems --- Variations, Calculus of --- Maxima and minima --- Nonconvex programming. --- Global optimization --- Non-convex programming --- Programming (Mathematics) --- Optimització matemàtica --- Estadística bayesiana --- Estadística de Bayes --- Fórmula de Bayes --- Presa de decisions (Estadística bayesiana) --- Solució de Bayes --- Teorema de Bayes --- Teoria de la decisió estadística bayesiana --- Presa de decisions --- Mètodes de simulació --- Jocs d'estratègia (Matemàtica) --- Optimització combinatòria --- Programació dinàmica --- Programació (Matemàtica) --- Anàlisi de sistemes