Set-Valued Analysis"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 |
From inside the book
Results 1-5 of 30
... Optimization provides examples of problems where uniqueness of the solution is naturally lacking: Let W be a function from X x Y to R. We consider the family of minimization problems VyeF, V(y) := mfW(x,y) parametrized by parameters y ...
... optimization problems; — The Pontriagin principle when dealing with optimal control problems. After the advances of Functional Analysis, it was time to uncover the common fact behind all these results. It is still and always the Fermat ...
... optimization problems with constraints and play a key role in viability theory. In order to define space of normals, which in differential geometry consists of vectors othogonal to the tangent vector space, we are led to introduce the ...
... optimization is concerned, the Fermat Rule can be extended to any function by using these epiderivatives. Since they enjoy a rich calculus, we obtain in this way many necessary conditions for a minimum. This can be done by transferring ...
... optimization problems5. An interesting question arises: What are the connections between the (epigraphical) convergence of a sequence of functions and the (graphical) convergence of their gradients? We shall answer such questions ...