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


Klatte, Diethard; Kummer, Bernd (2002). Nonsmooth Equations in Optimization: Regularity, Calculus, Methods and Applications (Nonconvex Optimization and Its Applications. Dordrecht, Boston, London: Kluwer Academic Publishers.

Abstract

The book establishes links between regularity and derivative concepts of nonsmooth analysis and studies of solution methods and stability for optimization, complementarity and equilibrium problems. In developing necessary tools, it presents, in particular, (i) an extended analysis of Lipschitz functions and the calculus of their generalized derivatives, including regularity, successive approximation and implicit functions for multivalued mappings, (ii) a unified theory of Lipschitzian critical points in optimization and other variational problems, with relations to reformulations by penalty, barrier and NCP functions, (iii) an analysis of generalized Newton methods based on linear and nonlinear approximations, (iv) the interpretation of hypotheses, generalized derivatives and solution methods in terms of original data and quadratic approximations, (v) a rich collection of instructive examples and exercises. It is written for researchers, graduate students and practitioners in various fields of applied mathematics, engineering, OR and economics, but also for university teachers and advanced students who wish to get insights into problems, potentials and recent developments of this rich and thriving area of nonlinear analysis and optimization.

The book establishes links between regularity and derivative concepts of nonsmooth analysis and studies of solution methods and stability for optimization, complementarity and equilibrium problems. In developing necessary tools, it presents, in particular, (i) an extended analysis of Lipschitz functions and the calculus of their generalized derivatives, including regularity, successive approximation and implicit functions for multivalued mappings, (ii) a unified theory of Lipschitzian critical points in optimization and other variational problems, with relations to reformulations by penalty, barrier and NCP functions, (iii) an analysis of generalized Newton methods based on linear and nonlinear approximations, (iv) the interpretation of hypotheses, generalized derivatives and solution methods in terms of original data and quadratic approximations, (v) a rich collection of instructive examples and exercises. It is written for researchers, graduate students and practitioners in various fields of applied mathematics, engineering, OR and economics, but also for university teachers and advanced students who wish to get insights into problems, potentials and recent developments of this rich and thriving area of nonlinear analysis and optimization.

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Additional indexing

Item Type:Monograph
Communities & Collections:03 Faculty of Economics > Department of Business Administration
Dewey Decimal Classification:330 Economics
Language:English
Date:2002
Deposited On:19 Dec 2013 15:08
Last Modified:05 Apr 2016 17:17
Publisher:Kluwer Academic Publishers
Series Name:Nonconvex Optimization and Its Applications
Volume:60
Number of Pages:356
ISBN:1-4020-0550-4
Other Identification Number:merlin-id:8754

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