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Presenting the latest findings in the field of numerical analysis and optimization, this volume balances pure research with practical applications of the subject. Accompanied by detailed tables, figures, and examinations of useful software tools, this volume will equip the reader to perform detailed and layered analysis of complex datasets. Many real-world complex problems can be formulated as optimization tasks. Such problems can be characterized as large scale, unconstrained, constrained, non-convex, non-differentiable, and discontinuous, and therefore require adequate computational methods, algorithms, and software tools. These same tools are often employed by researchers working in current IT hot topics such as big data, optimization and other complex numerical algorithms on the cloud, devising special techniques for supercomputing systems. The list of topics covered include, but are not limited to: numerical analysis, numerical optimization, numerical linear algebra, numerical differential equations, optimal control, approximation theory, applied mathematics, algorithms and software developments, derivative free optimization methods and programming models. The volume also examines challenging applications to various types of computational optimization methods which usually occur in statistics, econometrics, finance, physics, medicine, biology, engineering and industrial sciences.

Mathematics. --- Numerical Analysis. --- Partial Differential Equations. --- Ordinary Differential Equations. --- Optimization. --- Differential Equations. --- Differential equations, partial. --- Numerical analysis. --- Mathematical optimization. --- Mathématiques --- Analyse numérique --- Optimisation mathématique --- Engineering & Applied Sciences --- Applied Mathematics --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Differential equations. --- Partial differential equations. --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- 517.91 Differential equations --- Differential equations --- Partial differential equations

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Engineering design --- Mathematical optimization. --- Data processing. --- MATLAB. --- Agrotechnology and Food Sciences. Information and Communication Technology --- Data Processing, Database Management --- 681.3 --- Mathematical optimization --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Data processing 681.3 --- Data processing --- MATLAB --- MATLAB (Computer program) --- Matrix laboratory --- Data Processing, Database Management. --- 681.3. --- MATLAB (Computer file)

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Mathematics has many branches: there are the pure, the applied, and the applicable; the theoretical and the practical. There is mathematics for school, for college, and for industry. All these belong to the same family and are bound together by a "mathematical way of thinking." Some mathematicians devote themselves entirely to the well being of this family by preserving it, developing it, and teaching it to the next generation. Others use the familial attributes to help outsiders by taking up their problems and transforming them into mathematical questions in order to solve them. The work of these mathematicians is thus problem driven, based on mathematical models, and oriented on the goal of offering practicable solutions. This second group is sizeable; its members include almost all college graduates working in industry, in the private sector, or in the Fraunhofer Institutes, for example. This group is hardly visible, however, and one seldom hears its voices either. This book remedies this situation by relating how the scientists of the first Fraunhofer Institute for Mathematics, the ITWM in Kaiserslautern, go about their daily work. In so doing, it illustrates how extraordinarily successful today's mathematics is in helping solve industrial problems and reveals what lies behind this success. Finally, it describes how this exciting field of problem-driven mathematics can be integrated into classroom instruction, thus helping to bring it the recognition it so richly deserves.

Applied Mathematics --- Engineering & Applied Sciences --- Mathematics. --- Applied mathematics. --- Math --- Mathematical models. --- Mathematical optimization. --- Engineering mathematics. --- Mathematical Modeling and Industrial Mathematics. --- Appl.Mathematics/Computational Methods of Engineering. --- Optimization. --- Science --- Mathematical and Computational Engineering. --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Engineering --- Engineering analysis --- Mathematics --- Models, Mathematical

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This tutorial text gives a unifying perspective on machine learning by covering both probabilistic and deterministic approaches -which are based on optimization techniques – together with the Bayesian inference approach, whose essence lies in the use of a hierarchy of probabilistic models. The book presents the major machine learning methods as they have been developed in different disciplines, such as statistics, statistical and adaptive signal processing and computer science. Focusing on the physical reasoning behind the mathematics, all the various methods and techniques are explained in depth, supported by examples and problems, giving an invaluable resource to the student and researcher for understanding and applying machine learning concepts. The book builds carefully from the basic classical methods  to  the most recent trends, with chapters written to be as self-contained as possible, making the text suitable for  different courses: pattern recognition, statistical/adaptive signal processing, statistical/Bayesian learning, as well as short courses on sparse modeling, deep learning, and probabilistic graphical models. All major classical techniques: Mean/Least-Squares regression and filtering, Kalman filtering, stochastic approximation and online learning, Bayesian classification, decision trees, logistic regression and boosting methods. The latest trends: Sparsity, convex analysis and optimization, online distributed algorithms, learning in RKH spaces, Bayesian inference, graphical and hidden Markov models, particle filtering, deep learning, dictionary learning and latent variables modeling. Case studies - protein folding prediction, optical character recognition, text authorship identification, fMRI data analysis, change point detection, hyperspectral image unmixing, target localization, channel equalization and echo cancellation, show how the theory can be applied. MATLAB code for all the main algorithms are available on an accompanying website, enabling the reader to experiment with the code.

Numerical methods of optimisation --- Operational research. Game theory --- Mathematical statistics --- Machine elements --- Machine learning. --- Mathematical optimization. --- Bayesian statistical decision theory. --- Bayes' solution --- Bayesian analysis --- Statistical decision --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Learning, Machine --- Artificial intelligence --- Machine theory --- Machine learning --- Bayesian statistical decision theory --- Mathematical optimization --- Machine learning - Mathematical models

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This is a short tract on the essentials of differential and symplectic geometry together with a basic introduction to several applications of this rich framework: analytical mechanics, the calculus of variations, conjugate points & Morse index, and other physical topics. A central feature is the systematic utilization of Lagrangian submanifolds and their Maslov-Hörmander generating functions. Following this line of thought, first introduced by Wlodemierz Tulczyjew, geometric solutions of Hamilton-Jacobi equations, Hamiltonian vector fields and canonical transformations are described by suitable Lagrangian submanifolds belonging to distinct well-defined symplectic structures. This unified point of view has been particularly fruitful in symplectic topology, which is the modern Hamiltonian environment for the calculus of variations, yielding sharp sufficient existence conditions. This line of investigation was initiated by Claude Viterbo in 1992; here, some primary consequences of this theory are exposed in Chapter 8: aspects of Poincaré's last geometric theorem and the Arnol'd conjecture are introduced. In Chapter 7 elements of the global asymptotic treatment of the highly oscillating integrals for the Schrödinger equation are discussed: as is well known, this eventually leads to the theory of Fourier Integral Operators. This short handbook is directed toward graduate students in Mathematics and Physics and to all those who desire a quick introduction to these beautiful subjects.

Mathematics. --- Mathematical Physics. --- Differential Geometry. --- Calculus of Variations and Optimal Control; Optimization. --- Global differential geometry. --- Mathematical optimization. --- Mathématiques --- Géométrie différentielle globale --- Optimisation mathématique --- Engineering & Applied Sciences --- Civil & Environmental Engineering --- Applied Physics --- Operations Research --- Symplectic manifolds. --- Manifolds, Symplectic --- Differential geometry. --- Calculus of variations. --- Mathematical physics. --- Geometry, Differential --- Manifolds (Mathematics) --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Isoperimetrical problems --- Variations, Calculus of --- Differential geometry --- Physical mathematics --- Physics --- Mathematics --- Geometry, Differential.