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 84
... derivative of a (polynomial) function vanishes when it reaches an extremum. (This is Fermat's Rule, which remains the main strategy for obtaining necessary conditions of op- timality, from mathematical programming to calculus of ...
... Derivatives of Single- Valued Maps 93 3.4.2 Constrained Inverse Function Theorems .... 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 ...
... Derivatives of Set- Valued Maps 179 5.1 Contingent Derivatives 181 5.2 Adjacent and Circatangent Derivatives 189 5.2.1 Definitions and Elementary Properties 189 5.2.2 Limits of Differential Quotients 191 5.2.3 Derivatives of monotone ...
... Derivative 183 6.1 Epigraph of the Contingent Derivative 227 9.1 Approximate Selection of an Upper Semicontinuous Map359 9.2 Illustration of the proof 370 List of Tables 2.1 Properties of Support Functions 66 4.1 Properties of ...
... derivative of a function vanishes at points where it achieves an extremum) were needed to replace optimization problems by the resolution of equations. 1 "Je desire seulement qu'il [Descartes] sache que nos questions de Maximis et ...
Contents
1 | |
02pdf | 15 |
03pdf | 55 |
04pdf | 77 |
05pdf | 117 |
06pdf | 179 |
07pdf | 219 |
08pdf | 265 |
09pdf | 303 |
10pdf | 353 |
11pdf | 383 |
12pdf | 411 |