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To this reviewer's knowledge, this is the first book accessible to the upper division undergraduate or beginning graduate student that surveys linear programming from the Simplex Method via the Ellipsoid algorithm to Karmarkar's algorithm. Moreover, its point of view is algorithmic and thus it provides both a history and a case history of work in complexity theory. The presentation is admirable; Karloff's style is informal (even humorous at times) without sacrificing anything necessary for understanding. Diagrams (including horizontal brackets that group terms) aid in providing clarity. The end-of-chapter notes are helpful...Recommended highly for acquisition, since it is not only a textbook, but can also be used for independent reading and study - "Choice Reviews".'The reader will be well served by reading the monograph from cover to cover. The author succeeds in providing a concise, readable, understandable introduction to modern linear programming' - "Mathematics of Computing". 'This is a textbook intended for advanced undergraduate or graduate students. It contains both theory and computational practice. After preliminary discussion of linear algebra and geometry, it describes the simplex algorithm, duality, the ellipsoid algorithm (Khachiyan's algorithm) and Karmarkar's algorithm' - "Zentralblatt Math". 'The exposition is clear and elementary; it also contains many exercises and illustrations' - "Mathematical Reviews". 'A self-contained, concise mathematical introduction to the theory of linear programming' - "Journal of Economic Literature".
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'An elegantly written, introductory overview of the field, with a near perfect choice of what to include and what not, enlivened in places by historical tidbits and made eminently readable throughout by crisp language. It has succeeded in doing the near-impossible - it has made a subject which is generally inhospitable to nonspecialists because of its 'family jargon' appear nonintimidating even to a beginning graduate student' - "The Journal of the Indian Institute of Science". 'The book under review gives a comprehensive treatment of basically everything in mathematics that can be named multivalued/set-valued analysis. It includes! results with many historical comments giving the reader a sound perspective to look at the subject! The book is highly recommended for mathematicians and graduate students who will find here a very comprehensive treatment of set-valued analysis' - "Mathematical Reviews". 'I recommend this book as one to dig into with considerable pleasure when one already knows the subject..."Set-Valued Analysis" goes a long way toward providing a much needed basic resource on the subject' - "Bulletin of the American Mathematical Society". 'This book provides a thorough introduction to multivalued or set-valued analysis...Examples in many branches of mathematics, given in the introduction, prevail [upon] the reader the indispensability [of dealing] with sequences of sets and set-valued maps! The style is lively and vigorous, the relevant historical comments and suggestive overviews increase the interest for this work...Graduate students and mathematicians of every persuasion will welcome this unparalleled guide to set-valued analysis' - "Zentralblatt Math".
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This work examines viability theory and its applications to control theory and differential games. The emphasis is on the construction of feedbacks and dynamical systems by myopic optimization methods. Systems of first-order partial differential inclusions, whose solutions are feedbacks, are constructed and investigated. Basic results are then extended to the case of fuzzy control problems, distributed control problems, and control systems with delays and memory. Aimed at graduate students and research mathematicians, both pure and applied, this book offers specialists in control and nonlinear systems tools to take into account general state constraints. Viability theory also allows researchers in other disciplines?artificial intelligence, economics, game theory, theoretical biology, population genetics, cognitive sciences?to go beyond deterministic models by studying them in a dynamical or evolutionary perspective in an uncertain environment. "The book is a compendium of the state of knowledge about viability...Mathematically, the book should be accessible to anyone who has had basic graduate courses in modern analysis and functional analysis?The concepts are defined and many proofs of the requisite results are reproduced here, making the present book essentially self-contained." (Bulletin of the AMS) "Because of the wide scope, the book is an ideal reference for people encountering problems related to viability theory in their research?It gives a very thorough mathematical presentation. Very useful for anybody confronted with viability constraints." (Mededelingen van het Wiskundig Genootschap)
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