Springer Science & Business Media, Mar 2, 2009 - Science - 461 pages
"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."
"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."
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(This is Fermat's Rule, which remains the main strategy for obtaining necessary conditions of op- timality, from mathematical programming to calculus of variations to optimal control). Fermat also was the first to discover the ...
94 3.4.3 Pointwise Stability Conditions 101 3.4.4 Local Uniqueness 103 3.5 Monotone and Maximal Monotone Maps 104 3.5.1 Monotone Maps 104 3.5.2 Maximal Monotone Maps 106 3.5.3 Yosida Approximations Ill 3.6 Eigenvectors of Closed Convex ...
... when necessary conditions (the Fermat rule1 , stating that the derivative of a function vanishes at points where it achieves an extremum) were needed to replace optimization problems by the resolution of equations.
... involved in the sufficient conditions for the existence of an equilibrium and for the stability of solutions to equations with constraints. They also appear in the formulation of necessary conditions in optimization problems with ...
Since they enjoy a rich calculus, we obtain in this way many necessary conditions for a minimum. This can be done by transferring the set-valued differential calculus to what can be called an epidifferential calculus.