Nonsmooth Equations in Optimization | Regularity, Calculus, Methods and Applications

Diethard Klatte (u. a.)

ISBN 10: 1402005504 / ISBN 13: 9781402005503

Published by Springer, 2002

Nonsmooth Equations in Optimization | Regularity, Calculus, Methods and Applications | Diethard Klatte (u. a.) | Buch | Nonconvex Optimization and Its Applications | xxviii | Englisch | 2002 | Springer | EAN 9781402005503 | Verantwortliche Person für die EU: Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg, juergen[dot]hartmann[at]springer[dot]com | Anbieter: preigu Print on Demand. Seller Inventory # 102580128

Synopsis:

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.

Bibliographic Details

Title: Nonsmooth Equations in Optimization | ...
Publisher: Springer
Publication Date: 2002
Binding: Buch
Condition: Neu