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Convex functions --- Monotonic functions --- Geometry --- Operational research. Game theory --- Mathematical optimization. --- Operations research. --- Decision making. --- Calculus of variations. --- Optimization. --- Operations Research/Decision Theory. --- Calculus of Variations and Optimal Control; Optimization. --- Isoperimetrical problems --- Variations, Calculus of --- Maxima and minima --- Deciding --- Decision (Psychology) --- Decision analysis --- Decision processes --- Making decisions --- Management --- Management decisions --- Choice (Psychology) --- Problem solving --- Operational analysis --- Operational research --- Industrial engineering --- Management science --- Research --- System theory --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Operations research --- Simulation methods --- System analysis --- Decision making

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This book is an abridged version of our two-volume opus Convex Analysis and Minimization Algorithms [18], about which we have received very positive feedback from users, readers, lecturers ever since it was published - by Springer-Verlag in 1993. Its pedagogical qualities were particularly appreciated, in the combination with a rather advanced technical material. Now [18] hasa dual but clearly defined nature: - an introduction to the basic concepts in convex analysis, - a study of convex minimization problems (with an emphasis on numerical al- rithms), and insists on their mutual interpenetration. It is our feeling that the above basic introduction is much needed in the scientific community. This is the motivation for the present edition, our intention being to create a tool useful to teach convex anal­ ysis. We have thus extracted from [18] its "backbone" devoted to convex analysis, namely ChapsIII-VI and X. Apart from some local improvements, the present text is mostly a copy of the corresponding chapters. The main difference is that we have deleted material deemed too advanced for an introduction, or too closely attached to numerical algorithms. Further, we have included exercises, whose degree of difficulty is suggested by 0, I or 2 stars *. Finally, the index has been considerably enriched. Just as in [18], each chapter is presented as a "lesson", in the sense of our old masters, treating of a given subject in its entirety.

Convex sets. --- Convex functions --- Convex sets --- Mathematical analysis --- Computers. --- Mathematical analysis. --- Analysis (Mathematics). --- Calculus of variations. --- Operations research. --- Management science. --- System theory. --- Theory of Computation. --- Analysis. --- Calculus of Variations and Optimal Control; Optimization. --- Operations Research, Management Science. --- Systems Theory, Control. --- Systems, Theory of --- Systems science --- Science --- Quantitative business analysis --- Management --- Problem solving --- Operations research --- Statistical decision --- Operational analysis --- Operational research --- Industrial engineering --- Management science --- Research --- System theory --- Isoperimetrical problems --- Variations, Calculus of --- Maxima and minima --- 517.1 Mathematical analysis --- Automatic computers --- Automatic data processors --- Computer hardware --- Computing machines (Computers) --- Electronic brains --- Electronic calculating-machines --- Electronic computers --- Hardware, Computer --- Computer systems --- Cybernetics --- Machine theory --- Calculators --- Cyberspace --- Philosophy --- Analyse convexe --- Programmation mathematique --- Programmation convexe

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The goal of the Encyclopedia of Operations Research and Management Science is to provide decision makers and problem solvers in business, industry, government and academia with a comprehensive overview of the wide range of ideas, methodologies, and synergistic forces that combine to form the pre-eminent decision-aiding fields of operations research and management science (OR/MS). The Second Edition is a further extension of this goal - which through addressing and solving a wide range of problems - OR/MS methodologies continue to flourish and grow. This is a field that is used extensively throughout the applied sciences, and, because of this, the new edition has added topics in the following areas: Analytic Network Process; Call Centers; Certainty Equivalence; Comb. Optimization by Simulated CE; Computational Organization; Constraint Programming; Data Mining; Degeneracy Graphs; Economic Order Q Extensions; Educational Issues in B-Schools; Electronic Commerce; Financial Markets; Global Climate Change; Hidden Markov Models; History of Early British OR; Implementation for Public Sector; Info Tech Benefits; Interactive Multi-Objective Math. Programming; Knapsacks with Nonlinearities; Little's Law in Distribution Form; Military Ops Other than War; Multivariate Quality Control; Perturbation Analysis; Simulation Metamodeling; Simulation Optimization; Supply Chain Management; Theory of Constraints; Timetabling. The intended audience of the Encyclopedia of Operations Research and Management Science is technically diverse and wide; it includes anyone concerned with the science, techniques, and ideas of how one makes decisions. As this audience encompasses many professions, educational backgrounds and skills, we were attentive to the form, format and scope of the articles. Thus, the articles are designed to serve as initial sources of information for all such readers, with special emphasis on the needs of students. Each article provides a background or history of the topic, describes relevant applications, overviews present and future trends, and lists seminal and current references. To allow for variety in exposition, the authors were instructed to present their material from both research and applied perspectives. The Encyclopedia has been organized into specific topics that collectively encompass the foundations, applications, and emerging elements of this ever-changing field. We also wanted to establish the close associations that OR/MS has maintained with other scientific endeavors, with special emphasis on its symbiotic relationships to computer science, information processing, and mathematics. Based on our broad view of OR/MS, we commissioned 228 major expository articles and complemented them by numerous entries: descriptions, discussions, definitions, and abbreviations. The connections between topics are highlighted by an entry's final `See' statement, as appropriate. Each topical article provides a background or history of the topic, describes relevant applications, overviews present and future trends, and lists seminal and current references. Of significant importance is that each contributed topic has been authored by a leading authoritative researcher on that particular topic.

Operational research. Game theory --- Quantitative business analysis --- Business. --- Production management. --- Operations research. --- Decision making. --- Mathematical models. --- Calculus of variations. --- Business and Management. --- Operation Research/Decision Theory. --- Operations Management. --- Calculus of Variations and Optimal Control; Optimization. --- Mathematical Modeling and Industrial Mathematics. --- Isoperimetrical problems --- Variations, Calculus of --- Maxima and minima --- Models, Mathematical --- Simulation methods --- Deciding --- Decision (Psychology) --- Decision analysis --- Decision processes --- Making decisions --- Management --- Management decisions --- Choice (Psychology) --- Problem solving --- Operational analysis --- Operational research --- Industrial engineering --- Management science --- Research --- System theory --- Manufacturing management --- Industrial management --- Trade --- Economics --- Commerce --- Decision making --- Operations research --- 519.8 --- 519.8 Operational research --- Statistical decision --- Planning (firm) --- Mathematical optimization. --- Operations Research/Decision Theory. --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- System analysis --- Operations research - Encyclopedias --- Management science - Encyclopedias --- Operations Research and Decision Theory. --- Calculus of Variations and Optimization.

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Partial differential equations and variational methods were introduced into image processing about 15 years ago, and intensive research has been carried out since then. The main goal of this work is to present the variety of image analysis applications and the precise mathematics involved. It is intended for two audiences. The first is the mathematical community, to show the contribution of mathematics to this domain and to highlight some unresolved theoretical questions. The second is the computer vision community, to present a clear, self-contained, and global overview of the mathematics involved in image processing problems. The book is divided into five main parts. Chapter 1 is a detailed overview. Chapter 2 describes and illustrates most of the mathematical notions found throughout the work. Chapters 3 and 4 examine how PDEs and variational methods can be successfully applied in image restoration and segmentation processes. Chapter 5, which is more applied, describes some challenging computer vision problems, such as sequence analysis or classification. This book will be useful to researchers and graduate students in mathematics and computer vision.

Image processing --- Mathematics. --- Image processing: image displays image processing software (Computing methododologies) --- 681.3*I4 Image processing: image displays image processing software (Computing methododologies) --- Computers. --- Image processing. --- Mathematical analysis. --- Analysis (Mathematics). --- Applied mathematics. --- Engineering mathematics. --- System theory. --- Calculus of variations. --- Analysis. --- Applications of Mathematics. --- Calculus of Variations and Optimal Control; Optimization. --- Systems Theory, Control. --- Computing Methodologies. --- Image Processing and Computer Vision. --- 681.3*I4 --- 517.97 --- 517.97 Calculus of variations. Mathematical theory of control --- Calculus of variations. Mathematical theory of control --- 681.3*I4 Image processing: image displays; image processing software (Computing methododologies) --- Image processing: image displays; image processing software (Computing methododologies) --- Global analysis (Mathematics). --- Mathematical optimization. --- Systems theory. --- Artificial intelligence. --- Computer vision. --- Artificial Intelligence. --- Optical data processing. --- Optical computing --- Visual data processing --- Bionics --- Electronic data processing --- Integrated optics --- Photonics --- Computers --- AI (Artificial intelligence) --- Artificial thinking --- Electronic brains --- Intellectronics --- Intelligence, Artificial --- Intelligent machines --- Machine intelligence --- Thinking, Artificial --- Cognitive science --- Digital computer simulation --- Logic machines --- Machine theory --- Self-organizing systems --- Simulation methods --- Fifth generation computers --- Neural computers --- Systems, Theory of --- Systems science --- Science --- Isoperimetrical problems --- Variations, Calculus of --- Maxima and minima --- Engineering --- Engineering analysis --- Mathematical analysis --- 517.1 Mathematical analysis --- Optical equipment --- Philosophy --- Mathematics