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This book is devoted to the recent progress on the turnpike theory. The turnpike property was discovered by Paul A. Samuelson, who applied it to problems in mathematical economics in 1949. These properties were studied for optimal trajectories of models of economic dynamics determined by convex processes. In this monograph the author, a leading expert in modern turnpike theory, presents a number of results concerning the turnpike properties in the calculus of variations and optimal control which were obtained in the last ten years. These results show that the turnpike properties form a general phenomenon which holds for various classes of variational problems and optimal control problems. The book should help to correct the misapprehension that turnpike properties are only special features of some narrow classes of convex problems of mathematical economics. Audience This book is intended for mathematicians interested in optimal control, calculus of variations, game theory and mathematical economics.

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

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Robust design—that is, managing design uncertainties such as model uncertainty or parametric uncertainty—is the often unpleasant issue crucial in much multidisciplinary optimal design work. Recently, there has been enormous practical interest in strategies for applying optimization tools to the development of robust solutions and designs in several areas, including aerodynamics, the integration of sensing (e.g., laser radars, vision-based systems, and millimeter-wave radars) and control, cooperative control with poorly modeled uncertainty, cascading failures in military and civilian applications, multi-mode seekers/sensor fusion, and data association problems and tracking systems. The contributions to this book explore these different strategies. The expression "optimization-directed” in this book’s title is meant to suggest that the focus is not agonizing over whether optimization strategies identify a true global optimum, but rather whether these strategies make significant design improvements. Audience .

System theory. --- Mathematical optimization. --- Programming (Mathematics) --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Systems, Theory of --- Systems science --- Science --- Philosophy --- Mathematical programming --- Goal programming --- Algorithms --- Functional equations --- Mathematical optimization --- Mathematics. --- Systems theory. --- Optimization. --- Applications of Mathematics. --- Systems Theory, Control. --- Math --- Applied mathematics. --- Engineering mathematics. --- Engineering --- Engineering analysis --- Mathematics

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This comprehensive textbook on combinatorial optimization puts special emphasis on theoretical results and algorithms with provably good performance, in contrast to heuristics. It has arisen as the basis of several courses on combinatorial optimization and more special topics at graduate level. Since the complete book contains enough material for at least four semesters (4 hours a week), one usually selects material in a suitable way. The book contains complete but concise proofs, also for many deep results, some of which did not appear in a book before. Many very recent topics are covered as well, and many references are provided. Thus this book represents the state of the art of combinatorial optimization. This third edition contains a new chapter on facility location problems, an area which has been extremely active in the past few years. Furthermore there are several new sections and further material on various topics. New exercises and updates in the bibliography were added. From the reviews of the 2nd edition: "This book on combinatorial optimization is a beautiful example of the ideal textbook." Operations Research Letters 33 (2005), p.216-217 "The second edition (with corrections and many updates) of this very recommendable book documents the relevant knowledge on combinatorial optimization and records those problems and algorithms that define this discipline today. To read this is very stimulating for all the researchers, practitioners, and students interested in combinatorial optimization." OR News 19 (2003), p.42 .

Combinatorial optimization. --- Mathematics. --- Computer science --- Calculus of variations. --- Combinatorics. --- Calculus of Variations and Optimal Control; Optimization. --- Mathematics of Computing. --- Optimization, Combinatorial --- Combinatorial analysis --- Mathematical optimization --- Mathematical optimization. --- Computer science. --- Informatics --- Science --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Combinatorics --- Algebra --- Computer science—Mathematics. --- Isoperimetrical problems --- Variations, Calculus of --- Combinatorial analysis.

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Mathematical optimization --- Combinatorial optimization --- Optimisation mathématique --- Optimisation combinatoire --- Optimaliseren. --- Optimization, Combinatorial --- Combinatorial optimization. --- Mathematical optimization. --- Combinatorial analysis --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Mathematical Sciences --- Applied Mathematics --- Optimizaton. --- Operations Research --- Optimització matemàtica --- Optimització combinatòria --- Optimisation mathématique --- Optimització matemàtica. --- Optimització combinatòria.

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This book, a result of the authors’ teaching and research experience in various universities and institutes over the past ten years, can be used as a textbook for an optimization course for graduates and senior undergraduates. It systematically describes optimization theory and several powerful methods, including recent results. For most methods, the authors discuss an idea’s motivation, study the derivation, establish the global and local convergence, describe algorithmic steps, and discuss the numerical performance. The book deals with both theory and algorithms of optimization concurrently. It also contains an extensive bibliography with 366 references. Finally, apart from its use for teaching, Optimization Theory and Methods is also very beneficial for doing research. Audience This book is intended for senior students, graduates, teachers, and researchers in optimization, operations research, computational mathematics, applied mathematics, and some engineering and economics. It will also be useful for scientists in engineering and economics.

Nonlinear programming. --- Mathematical optimization. --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Programming (Mathematics) --- Numerical analysis. --- Computer science. --- Optimization. --- Numerical Analysis. --- Operations Research, Management Science. --- Computational Science and Engineering. --- Informatics --- Science --- Operations research. --- Management science. --- Computer mathematics. --- Computer mathematics --- Electronic data processing --- Mathematics --- Quantitative business analysis --- Management --- Problem solving --- Statistical decision --- Operational analysis --- Operational research --- Industrial engineering --- Management science --- Research --- System theory