Nonsmooth Equations in Optimization: Regularity, Calculus, Methods and Applications (Nonconvex Optimization and Its Applications Volume 60)

Klatte, Diethard; Kummer, Bernd;

ISBN 10: 1402005504 / ISBN 13: 9781402005503

Published by Kluwer Academic Publishers, Dordrecht, The Netherlands, 2002

About this Item

329pp. Spine is cocked. Tips and spine ends are bumped and rubbed. Boards have scratches. Text is unmarked. 1402005504. Seller Inventory # 34116

Bibliographic Details

Title: Nonsmooth Equations in Optimization: ...

Publisher: Kluwer Academic Publishers, Dordrecht, The Netherlands

Publication Date: 2002

Binding: Hardcover

Condition: Very Good Minus

Dust Jacket Condition: No Dust Jacket

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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.