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Nonconvex Optimization and Its Applications

Nonsmooth Equations in Optimization

Regularity, Calculus, Methods and Applications

Authors: Klatte, Diethard, Kummer, B.

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About this book

Many questions dealing with solvability, stability and solution methods for va- ational inequalities or equilibrium, optimization and complementarity problems lead to the analysis of certain (perturbed) equations. This often requires a - formulation of the initial model being under consideration. Due to the specific of the original problem, the resulting equation is usually either not differ- tiable (even if the data of the original model are smooth), or it does not satisfy the assumptions of the classical implicit function theorem. This phenomenon is the main reason why a considerable analytical inst- ment dealing with generalized equations (i.e., with finding zeros of multivalued mappings) and nonsmooth equations (i.e., the defining functions are not c- tinuously differentiable) has been developed during the last 20 years, and that under very different viewpoints and assumptions. In this theory, the classical hypotheses of convex analysis, in particular, monotonicity and convexity, have been weakened or dropped, and the scope of possible applications seems to be quite large. Briefly, this discipline is often called nonsmooth analysis, sometimes also variational analysis. Our book fits into this discipline, however, our main intention is to develop the analytical theory in close connection with the needs of applications in optimization and related subjects. Main Topics of the Book 1. Extended analysis of Lipschitz functions and their generalized derivatives, including ”Newton maps” and regularity of multivalued mappings. 2. Principle of successive approximation under metric regularity and its - plication to implicit functions.

Table of contents (12 chapters)

Table of contents (12 chapters)

Buy this book

eBook $149.00
price for USA in USD (gross)
  • ISBN 978-0-306-47616-7
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $199.99
price for USA in USD
  • ISBN 978-1-4020-0550-3
  • Free shipping for individuals worldwide
  • Immediate ebook access, if available*, with your print order
  • Usually dispatched within 3 to 5 business days.
Softcover $199.99
price for USA in USD
  • ISBN 978-1-4419-5218-9
  • Free shipping for individuals worldwide
  • Immediate ebook access, if available*, with your print order
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Nonsmooth Equations in Optimization
Book Subtitle
Regularity, Calculus, Methods and Applications
Authors
Series Title
Nonconvex Optimization and Its Applications
Series Volume
60
Copyright
2002
Publisher
Springer US
Copyright Holder
Springer Science+Business Media Dordrecht
eBook ISBN
978-0-306-47616-7
DOI
10.1007/b130810
Hardcover ISBN
978-1-4020-0550-3
Softcover ISBN
978-1-4419-5218-9
Series ISSN
1571-568X
Edition Number
1
Number of Pages
XXVIII, 333
Topics

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