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Computational optimization is an active and important area of study, practice, and research today. It covers a wide range of applications in engineering, science, and industry. It provides solutions to a variety of real-life problems in the fields of health, business, government, military, politics, security, education, and many more. This book compiles original and innovative findings on all aspects of computational optimization. It presents various examples of optimization including cost, energy, profits, outputs, performance, and efficiency. It also discusses different types of optimization problems like nonlinearity, multimodality, discontinuity, and uncertainty. Over thirteen chapters, the book provides researchers, practitioners, academicians, military professionals, government officials, and other industry professionals with an in-depth discussion of the latest advances in the field.

Constrained optimization.

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Optimization problems subject to constraints governed by partial differential equations (PDEs) are among the most challenging problems in the context of industrial, economical and medical applications. Almost the entire range of problems in this field of research was studied and further explored as part of the Deutsche Forschungsgemeinschaft (DFG) priority program 1253 on “Optimization with Partial Differential Equations” from 2006 to 2013. The investigations were motivated by the fascinating potential applications and challenging mathematical problems that arise in the field of PDE constrained optimization. New analytic and algorithmic paradigms have been developed, implemented and validated in the context of real-world applications. In this special volume, contributions from more than fifteen German universities combine the results of this interdisciplinary program with a focus on applied mathematics.   The book is divided into five sections on “Constrained Optimization, Identification and Control”, “Shape and Topology Optimization”, “Adaptivity and Model Reduction”, “Discretization: Concepts and Analysis” and “Applications”. Peer-reviewed research articles present the most recent results in the field of PDE constrained optimization and control problems. Informative survey articles give an overview of topics that set sustainable trends for future research. This makes this special volume interesting not only for mathematicians, but also for engineers and for natural and medical scientists working on processes that can be modeled by PDEs.

Constrained optimization. --- Differential equations, Partial. --- Partial differential equations --- Optimization, Constrained --- Mathematical optimization --- Differential equations, partial. --- Mathematical optimization. --- Computer science --- Partial Differential Equations. --- Optimization. --- Computational Mathematics and Numerical Analysis. --- Mathematics. --- Computer mathematics --- Discrete mathematics --- Electronic data processing --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Mathematics --- Partial differential equations. --- Computer mathematics.

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Numerical methods of optimisation --- Conjugate direction methods --- 519.6 --- 681.3*G16 --- Computational mathematics. Numerical analysis. Computer programming --- Optimization: constrained optimization; gradient methods; integer programming; least squares methods; linear programming; nonlinear programming (Numericalanalysis) --- 681.3*G16 Optimization: constrained optimization; gradient methods; integer programming; least squares methods; linear programming; nonlinear programming (Numericalanalysis) --- 519.6 Computational mathematics. Numerical analysis. Computer programming

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-519.85 --- Optimization: constrained optimization gradient methods integer programming least squares methods linear programming nonlinear programming (Numericalanalysis) --- 681.3*G16 Optimization: constrained optimization gradient methods integer programming least squares methods linear programming nonlinear programming (Numericalanalysis) --- Optimization: constrained optimization; gradient methods; integer programming; least squares methods; linear programming; nonlinear programming (Numericalanalysis) --- 681.3*G16 Optimization: constrained optimization; gradient methods; integer programming; least squares methods; linear programming; nonlinear programming (Numericalanalysis) --- Mathematical optimization --- 519.85 --- 519.8 --- 681.3*G16 --- 519.85 Mathematical programming --- Mathematical programming --- 519.8 Operational research --- Operational research --- Congresses --- Congresses. --- Optimisation mathématique --- Congrès --- Calculus of variations --- Operations research --- Programming (Mathematics) --- Programmation (mathématiques) --- Recherche opérationnelle --- Calcul des variations --- Optimisation mathématique --- Recherche opérationnelle. --- Optimisation mathématique. --- Mathematical optimization - Congresses --- Programmation (mathématiques) --- Recherche opérationnelle. --- Optimisation mathématique.

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Linear topological spaces --- Mathematical optimization --- Vector spaces --- Espaces vectoriels topologiques --- Optimisation mathématique --- Espaces vectoriels --- Linear spaces --- Linear vector spaces --- Topological linear spaces --- Topological vector spaces --- Vector topology --- Optimization: constrained optimization gradient methods integer programming least squares methods linear programming nonlinear programming (Numericalanalysis) --- 519 --- Linear topological spaces. --- Vector spaces. --- 681.3*G16 Optimization: constrained optimization gradient methods integer programming least squares methods linear programming nonlinear programming (Numericalanalysis) --- Mathematical optimization. --- lineaire algebra --- operations research --- 681.3*G16 --- 681.3*G16 Optimization: constrained optimization; gradient methods; integer programming; least squares methods; linear programming; nonlinear programming (Numericalanalysis) --- Optimization: constrained optimization; gradient methods; integer programming; least squares methods; linear programming; nonlinear programming (Numericalanalysis) --- Algebras, Linear --- Functional analysis --- Vector analysis --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Topology --- Nonlinear functional analysis. --- Analyse fonctionnelle non linéaire. --- Optimisation mathématique. --- Analyse numérique. --- Numerical analysis --- Numerical analysis. --- Analyse fonctionnelle non linéaire --- Analyse numérique --- Moindres carres