Nonsmooth Equations in Optimization - Regularity, Calculus, Methods and Applications (Paperback, Softcover reprint of the original 1st ed. 2002)

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.

General

Imprint:	Springer-Verlag New York
Country of origin:	United States
Series:	Nonconvex Optimization and Its Applications, 60
Release date:	December 2010
First published:	2002
Authors:	Diethard Klatte • B. Kummer
Dimensions:	235 x 155 x 19mm (L x W x T)
Format:	Paperback
Pages:	333
Edition:	Softcover reprint of the original 1st ed. 2002
ISBN-13:	978-1-4419-5218-9
Categories:	Books > Science & Mathematics > Mathematics > Numerical analysis Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Functional analysis Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Differential equations Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Calculus of variations Books > Science & Mathematics > Mathematics > Optimization > General
LSN:	1-4419-5218-7
Barcode:	9781441952189

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