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This book covers state-of-the-art optimization methods and their applications in wide range especially for researchers and practitioners who wish to improve their knowledge in this field. It consists of 13 chapters divided into two parts: (I) Engineering applications, which presents some new applications of different methods, and (II) Applications in various areas, where recent contributions of state-of-the-art optimization methods to diverse fields are presented.

Mathematical optimization. --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Optimization

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Stochastic processes. --- Business mathematics. --- Mathematical optimization. --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Arithmetic, Commercial --- Business --- Business arithmetic --- Business math --- Commercial arithmetic --- Finance --- Mathematics --- Random processes --- Probabilities

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This book presents results on the convergence behavior of algorithms which are known as vital tools for solving convex feasibility problems and common fixed point problems. The main goal for us in dealing with a known computational error is to find what approximate solution can be obtained and how many iterates one needs to find it. According to know results, these algorithms should converge to a solution. In this exposition, these algorithms are studied, taking into account computational errors which remain consistent in practice. In this case the convergence to a solution does not take place. We show that our algorithms generate a good approximate solution if computational errors are bounded from above by a small positive constant. Beginning with an introduction, this monograph moves on to study: · dynamic string-averaging methods for common fixed point problems in a Hilbert space · dynamic string methods for common fixed point problems in a metric space · dynamic string-averaging version of the proximal algorithm · common fixed point problems in metric spaces · common fixed point problems in the spaces with distances of the Bregman type · a proximal algorithm for finding a common zero of a family of maximal monotone operators · subgradient projections algorithms for convex feasibility problems in Hilbert spaces .

Mathematics. --- Operator theory. --- Numerical analysis. --- Calculus of variations. --- Calculus of Variations and Optimal Control; Optimization. --- Numerical Analysis. --- Operator Theory. --- Fixed point theory. --- Fixed point theorems (Topology) --- Nonlinear operators --- Coincidence theory (Mathematics) --- Mathematical optimization. --- Mathematical analysis --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Functional analysis --- Isoperimetrical problems --- Variations, Calculus of

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This textbook provides and introduction to numerical computing and its applications in science and engineering.  The topics covered include those usually found in an introductory course, as well as those that arise in data analysis.  This includes optimization and regression based methods using a singular value decomposition.  The emphasis is on problem solving, and there are numerous exercises throughout the text concerning applications in engineering and science.  The essential role of the mathematical theory underlying the methods is also considered, both for understanding how the method works, as well as how the error in the computation depends on the method being used.  The MATLAB codes used to produce most of the figures and data tables in the text are available on the author’s website and SpringerLink.

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

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This book is based on lectures from a one-year course at the Far Eastern Federal University (Vladivostok, Russia) as well as on workshops on optimal control offered to students at various mathematical departments at the university level. The main themes of the theory of linear and nonlinear systems are considered, including the basic problem of establishing the necessary and sufficient conditions of optimal processes. In the first part of the course, the theory of linear control systems is constructed on the basis of the separation theorem and the concept of a reachability set. The authors prove the closure of a reachability set in the class of piecewise continuous controls, and the problems of controllability, observability, identification, performance and terminal control are also considered. The second part of the course is devoted to nonlinear control systems. Using the method of variations and the Lagrange multipliers rule of nonlinear problems, the authors prove the Pontryagin maximum principle for problems with mobile ends of trajectories. Further exercises and a large number of additional tasks are provided for use as practical training in order for the reader to consolidate the theoretical material.

Mathematics. --- System theory. --- Calculus of variations. --- Calculus of Variations and Optimal Control; Optimization. --- Systems Theory, Control. --- Mathematical optimization. --- Systems theory. --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Control theory. --- Systems, Theory of --- Systems science --- Science --- Isoperimetrical problems --- Variations, Calculus of --- Philosophy