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This book is a self-contained account of the theory of viscosity solutions for first-order partial differential equations of Hamilton–Jacobi type and its interplay with Bellman’s dynamic programming approach to optimal control and differential games, as it developed after the beginning of the 1980s with the pioneering work of M. Crandall and P.L. Lions. The book will be of interest to scientists involved in the theory of optimal control of deterministic linear and nonlinear systems. In particular, it will appeal to system theorists wishing to learn about a mathematical theory providing a correct framework for the classical method of dynamic programming as well as mathematicians interested in new methods for first-order nonlinear PDEs. The work may be used by graduate students and researchers in control theory both as an introductory textbook and as an up-to-date reference book. "The exposition is self-contained, clearly written and mathematically precise. The exercises and open problems…will stimulate research in the field. The rich bibliography (over 530 titles) and the historical notes provide a useful guide to the area." — Mathematical Reviews "With an excellent printing and clear structure (including an extensive subject and symbol registry) the book offers a deep insight into the praxis and theory of optimal control for the mathematically skilled reader. All sections close with suggestions for exercises…Finally, with more than 500 cited references, an overview on the history and the main works of this modern mathematical discipline is given." — ZAA "The minimal mathematical background...the detailed and clear proofs, the elegant style of presentation, and the sets of proposed exercises at the end of each section recommend this book, in the first place, as a lecture course for graduate students and as a manual for beginners in the field. However, this status is largely extended by the presence of many advanced topics and results by the fairly comprehensive and up-to-date bibliography and, particularly, by the very pertinent historical and bibliographical comments at the end of each chapter. In my opinion, this book is yet another remarkable outcome of the brilliant Italian School of Mathematics." — Zentralblatt MATH "The book is based on some lecture notes taught by the authors at several universities...and selected parts of it can be used for graduate courses in optimal control. But it can be also used as a reference text for researchers (mathematicians and engineers)...In writing this book, the authors lend a great service to the mathematical community providing an accessible and rigorous treatment of a difficult subject." — Acta Applicandae Mathematicae.

Mathematical control systems --- Viscosity solutions --- Control theory --- Differential games --- System theory. --- Mathematical optimization. --- Partial differential equations. --- Systems Theory, Control. --- Optimization. --- Partial Differential Equations. --- Partial differential equations --- 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

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(revised) This is a textbook on classical mechanics at the intermediate level, but its main purpose is to serve as an introduction to a new mathematical language for physics called geometric algebra. Mechanics is most commonly formulated today in terms of the vector algebra developed by the American physicist J. Willard Gibbs, but for some applications of mechanics the algebra of complex numbers is more efficient than vector algebra, while in other applications matrix algebra works better. Geometric algebra integrates all these algebraic systems into a coherent mathematical language which not only retains the advantages of each special algebra but possesses powerful new capabilities. This book covers the fairly standard material for a course on the mechanics of particles and rigid bodies. However, it will be seen that geometric algebra brings new insights into the treatment of nearly every topic and produces simplifications that move the subject quickly to advanced levels. That has made it possible in this book to carry the treatment of two major topics in mechanics well beyond the level of other textbooks. A few words are in order about the unique treatment of these two topics, namely, rotational dynamics and celestial mechanics.

mechanica --- Algebraic geometry --- Mathematical physics --- Classical mechanics. Field theory --- Mechanics. --- Mécanique --- EPUB-LIV-FT SPRINGER-B --- Physics. --- Algebraic geometry. --- System theory. --- Observations, Astronomical. --- Astronomy --- Astronomy, Observations and Techniques. --- Algebraic Geometry. --- Systems Theory, Control. --- Observations. --- Geometry, algebraic. --- Systems theory. --- Classical Mechanics. --- Astronomy—Observations. --- Systems, Theory of --- Systems science --- Science --- Classical mechanics --- Newtonian mechanics --- Physics --- Dynamics --- Quantum theory --- Geometry --- Astronomical observations --- Observations, Astronomical --- Philosophy

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The 9th Belgian-French-German Conference on Optimization has been held in Namur (Belgium) on September 7-11, 1998. This volume is a collection of papers presented at this Conference. Originally, this Conference was a French-German Conference but this year, in accordance with the organizers' wishes, a third country, Belgium, has joined the founding members of the Conference. Hence the name: Belgian­ French-German Conference on Optimization. Since the very beginning, the purpose of these Conferences has been to bring together researchers working in the area of Optimization and partic­ ularly to encourage young researchers to present their work. Most of the participants come from the organizing countries. However the general ten­ dancy is to invite outside researchers to attend the meeting. So this year, among the 101 participants at this Conference, twenty researchers came from other countries. The general theme of the Conference is everything that concerns the area of Optimization without specification of particular topics. So theoretical as­ pects of Optimization, in addition to applications and algorithms of Opti­ mization, will be developed. However, and this point was very important for the organizers, the Conference must retain its convivial character. No more than two parallel sessions are organized. This would allow useful contacts between researchers to be promoted. The editors express their sincere thanks to all those who took part in this Conference. Their invaluable discussions have made this volume possible.

Mathematical statistics --- Mathematical optimization --- Civil & Environmental Engineering --- Engineering & Applied Sciences --- Operations Research --- AA / International- internationaal --- 305.976 --- NBB congres --- Algoritmen. Optimisatie. --- Conferences - Meetings --- Algoritmen. Optimisatie --- Operations research. --- Decision making. --- Calculus of variations. --- System theory. --- Operations Research/Decision Theory. --- Calculus of Variations and Optimal Control; Optimization. --- Systems Theory, Control. --- Systems, Theory of --- Systems science --- Science --- 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 --- Philosophy --- Decision making --- Programmation (mathématiques)

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This is a book for people interested in solving optimization problems. Because of the wide (and growing) use of optimization in science, engineering, economics, and industry, it is essential for students and practitioners alike to develop an understanding of optimization algorithms. Knowledge of the capabilities and limitations of these algorithms leads to a better understanding of their impact on various applications, and points the way to future research on improving and extending optimization algorithms and software. Our goal in this book is to give a comprehensive description of the most powerful, state-of-the-art, techniques for solving continuous optimization problems. By presenting the motivating ideas for each algorithm, we try to stimulate the reader’s intuition and make the technical details easier to follow. Formal mathematical requirements are kept to a minimum. Because of our focus on continuous problems, we have omitted discussion of important optimization topics such as discrete and stochastic optimization.

519.853 --- 519.65 --- Mathematical optimization --- #TELE:SISTA --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- 519.65 Approximation. Interpolation --- Approximation. Interpolation --- 519.853 Nonlinear programming. Relaxation methods --- Nonlinear programming. Relaxation methods --- Mathematical optimization. --- Numerical methods of optimisation --- Mathematics. --- Operations research. --- Decision making. --- System theory. --- Calculus of variations. --- Calculus of Variations and Optimal Control; Optimization. --- Systems Theory, Control. --- Operation Research/Decision Theory. --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Systems theory. --- Operations Research/Decision Theory. --- 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 --- Systems, Theory of --- Systems science --- Science --- Isoperimetrical problems --- Variations, Calculus of --- Decision making --- Philosophy --- Programmation (mathématiques) --- Programmation mathematique --- Methodes numeriques

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The volume is based on the papers that were presented at the Interna­ tional Conference Model-Based Reasoning in Scientific Discovery (MBR'98), held at the Collegio Ghislieri, University of Pavia, Pavia, Italy, in December 1998. The papers explore how scientific thinking uses models and explanatory reasoning to produce creative changes in theories and concepts. The study of diagnostic, visual, spatial, analogical, and temporal rea­ soning has demonstrated that there are many ways of performing intelligent and creative reasoning that cannot be described with the help only of tradi­ tional notions of reasoning such as classical logic. Traditional accounts of scientific reasoning have restricted the notion of reasoning primarily to de­ ductive and inductive arguments. Understanding the contribution of model­ ing practices to discovery and conceptual change in science requires ex­ panding scientific reasoning to include complex forms of creative reasoning that are not always successful and can lead to incorrect solutions. The study of these heuristic ways of reasoning is situated at the crossroads of philoso­ phy, artificial intelligence, cognitive psychology, and logic; that is, at the heart of cognitive science. There are several key ingredients common to the various forms of model­ based reasoning to be considered in this book. The models are intended as in­ terpretations of target physical systems, processes, phenomena, or situations. The models are retrieved or constructed on the basis of potentially satisfying salient constraints of the target domain.

Science --- Discoveries in science --- Qualitative reasoning --- Methodology --- Philosophy of science --- Computer simulation. --- Philosophy and science. --- System theory. --- Logic. --- Artificial intelligence. --- Cognitive psychology. --- Simulation and Modeling. --- Philosophy of Science. --- Systems Theory, Control. --- Artificial Intelligence. --- Cognitive Psychology. --- Psychology, Cognitive --- Cognitive science --- Psychology --- AI (Artificial intelligence) --- Artificial thinking --- Electronic brains --- Intellectronics --- Intelligence, Artificial --- Intelligent machines --- Machine intelligence --- Thinking, Artificial --- Bionics --- Digital computer simulation --- Electronic data processing --- Logic machines --- Machine theory --- Self-organizing systems --- Simulation methods --- Fifth generation computers --- Neural computers --- Argumentation --- Deduction (Logic) --- Deductive logic --- Dialectic (Logic) --- Logic, Deductive --- Intellect --- Philosophy --- Reasoning --- Thought and thinking --- Systems, Theory of --- Systems science --- Science and philosophy --- Computer modeling --- Computer models --- Modeling, Computer --- Models, Computer --- Simulation, Computer --- Electromechanical analogies --- Mathematical models --- Model-integrated computing --- Artificial intelligence --- Breakthroughs, Scientific --- Discoveries, Scientific --- Scientific breakthroughs --- Scientific discoveries --- Creative ability in science --- Research --- Science - Methodology - Congresses --- Discoveries in science - Congresses --- Qualitative reasoning - Congresses