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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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This book covers recent advances in image processing and imaging sciences from an optimization viewpoint, especially convex optimization with the goal of designing tractable algorithms. Throughout the handbook, the authors introduce topics on the most key aspects of image acquisition and processing that are based on the formulation and solution of novel optimization problems. The first part includes a review of the mathematical methods and foundations required, and covers topics in image quality optimization and assessment. The second part of the book discusses concepts in image formation and capture from color imaging to radar and multispectral imaging. The third part focuses on sparsity constrained optimization in image processing and vision and includes inverse problems such as image restoration and de-noising, image classification and recognition and learning-based problems pertinent to image understanding. Throughout, convex optimization techniques are shown to be a critically important mathematical tool for imaging science problems and applied extensively. Convex Optimization Methods in Imaging Science is the first book of its kind and will appeal to undergraduate and graduate students, industrial researchers and engineers and those generally interested in computational aspects of modern, real-world imaging and image processing problems.           Discusses recent developments in imaging science and provides tools for solving image processing and computer vision problems using convex optimization methods.          The reader is provided with the state of the art advancements in each imaging science problem that is covered and is directed to cutting edge theory and methods that should particularly help graduate students and young researchers in shaping their research.          Each chapter of the book covers a real-world imaging science problem while balancing both the theoretical and experimental aspects. The theoretical foundation of the problem is discussed thoroughly and then from a practical point of view, extensive validation and experiments are provided to enable the transition from theory to practice.          Topics of high current relevance are covered and include color and spectral imaging, dictionary learning for image classification and recovery, optimization and evaluation of image quality, sparsity constrained estimation for image processing and computer vision etc.        Provides insight on handling real-world imaging science problems that involve hard and non-convex objective functions through tractable convex optimization methods with the goal of providing a favorable performance-complexity trade-off. .

Computer science. --- Image processing. --- Computer Science. --- Image Processing and Computer Vision. --- Signal, Image and Speech Processing. --- Image processing --- Convex programming. --- Digital techniques. --- Programming (Mathematics) --- Digital image processing --- Digital electronics --- Computer vision. --- Machine vision --- Vision, Computer --- Artificial intelligence --- Pattern recognition systems --- Optical data processing. --- Signal processing. --- Speech processing systems. --- Computational linguistics --- Electronic systems --- Information theory --- Modulation theory --- Oral communication --- Speech --- Telecommunication --- Singing voice synthesizers --- Pictorial data processing --- Picture processing --- Processing, Image --- Imaging systems --- Optical data processing --- Processing, Signal --- Information measurement --- Signal theory (Telecommunication) --- Optical computing --- Visual data processing --- Bionics --- Electronic data processing --- Integrated optics --- Photonics --- Computers --- Optical equipment

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This text presents a multi-disciplined view of optimization, providing students and researchers with a thorough examination of algorithms, methods, and tools from diverse areas of optimization without introducing excessive theoretical detail. This second edition includes additional topics, including global optimization and a real-world case study using important concepts from each chapter. Key Features: Provides well-written self-contained chapters, including problem sets and exercises, making it ideal for the classroom setting; Introduces applied optimization to the hazardous waste blending problem; Explores linear programming, nonlinear programming, discrete optimization, global optimization, optimization under uncertainty, multi-objective optimization, optimal control and stochastic optimal control; Includes an extensive bibliography at the end of each chapter and an index; GAMS files of case studies for Chapters 2, 3, 4, 5, and 7 are linked to http://www.springer.com/math/book/978-0-387-76634-8; Solutions manual available upon adoptions. Introduction to Applied Optimization is intended for advanced undergraduate and graduate students and will benefit scientists from diverse areas, including engineers.

Mathematics. --- Calculus of Variations and Optimal Control; Optimization. --- Industrial Chemistry/Chemical Engineering. --- Appl.Mathematics/Computational Methods of Engineering. --- Systems Theory, Control. --- Business/Management Science, general. --- Chemical engineering. --- Systems theory. --- Mathematical optimization. --- Engineering mathematics. --- Economics. --- Mathématiques --- Génie chimique --- Optimisation mathématique --- Mathématiques de l'ingénieur --- Economie politique --- Convex programming. --- Finance -- Mathematical models. --- Finite element method. --- Civil & Environmental Engineering --- Engineering & Applied Sciences --- Operations Research --- Programming (Mathematics) --- Mathematical programming --- Goal programming --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Business. --- Management science. --- System theory. --- Calculus of variations. --- Applied mathematics. --- Optimization. --- Business and Management, general. --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Algorithms --- Functional equations --- Mathematical optimization --- Mathematical and Computational Engineering. --- Trade --- Economics --- Management --- Commerce --- Industrial management --- Engineering --- Engineering analysis --- Chemistry, Industrial --- Engineering, Chemical --- Industrial chemistry --- Chemistry, Technical --- Metallurgy --- Systems, Theory of --- Systems science --- Science --- Mathematics --- Philosophy --- Mathematical models. --- Isoperimetrical problems --- Variations, Calculus of --- Quantitative business analysis --- Problem solving --- Statistical decision