Quasidifferentiability and Nonsmooth Modelling in Mechanics, Engineering and Economics

by Vladimir F. Demyanov, Georgios E. Stavroulakis, L.N. Polyakova, P. D. Panagiotopoulos

Overview

Nonsmooth energy functions govern phenomena which occur frequently in nature and in all areas of life. They constitute a fascinating subject in mathematics and permit the rational understanding of yet unsolved or partially solved questions in mechanics, engineering and economics.
This is the first book to provide a complete and rigorous presentation of the quasidifferentiability approach to nonconvex, possibly nonsmooth, energy functions, of the derivation and study of the corresponding variational expressions in mechanics, engineering and economics, and of their numerical treatment. The new variational formulations derived are illustrated by many interesting numerical problems. The techniques presented will permit the reader to check any solution obtained by other heuristic techniques for nonconvex, nonsmooth energy problems. A civil, mechanical or aeronautical engineer can find in the book the only existing mathematically sound technique for the formulation and study of nonconvex, nonsmooth energy problems.
Audience: The book will be of interest to pure and applied mathematicians, physicists, researchers in mechanics, civil, mechanical and aeronautical engineers, structural analysts and software developers. It is also suitable for graduate courses in nonlinear mechanics, nonsmooth analysis, applied optimization, control, calculus of variations and computational mechanics.

Product Details

ISBN-13:	9781461368441
Publisher:	Springer US
Publication date:	11/15/2013
Series:	Nonconvex Optimization and Its Applications , #10
Edition description:	Softcover reprint of the original 1st ed. 1996
Pages:	349
Product dimensions:	6.10(w) x 9.25(h) x 0.03(d)

Table of Contents

Preface. Introduction. Guidelines for the Readers. 1. Nonsmooth Analysis. The One-Dimensional Case. 2. Quasidifferentiable Functions and Sets. Quasidifferentiable Optimization and Optimality Conditions. 3. Nonsmooth Mechanics I. Nonsmooth Modelling in Mechanics. 4. Nonsmooth Mechanics II. Variational Formulations Using Quasidifferentiability. 5. Additional Topics. Stability, Economics, Flow Problems, Dynamic Problems. 6. Nonsmooth Optimization Algorithms. Quasidifferentiable and Codifferentiable Optimization. 7. Nonsmooth Computational Mechanics I. Modelling and Applications. 8. Nonsmooth Computational Mechanics II. Algorithms and Examples. Subject Index.

Editorial Reviews

A rigorous presentation of the quasidifferentiability approach to nonconvex, possibly nonsmooth, energy functions, explaining the derivation and study of the corresponding variational expressions in mechanics, engineering and economics and their numerical treatment. Techniques presented allow readers to check any solution obtained by other heuristic techniques for nonconvex, nonsmooth energy problems. For pure and applied mathematicians, physicists, structural analysts, software developers, and civil, mechanical, and aeronautical engineers. Can also be used in graduate courses in nonlinear mechanics, applied optimization, calculus of variations, and computational mechanics. Annotation c. Book News, Inc., Portland, OR (booknews.com)

Booknews

‘... In view of the growing number of recent publications dealing with nonsmooth and set-valued modelling ... this book, which was written by a multidisciplinary group of authors, seems to be the first attempt to make nonsmooth modelling and set-valued techniques accessible to applied scientists by presenting the quasidifferentiable approach by means of concrete applications. ... The book provides significant help to scientists or graduate students who need an authoritative and understandable introduction to this field, and who would also, like to extend his/her ability to model nonsmooth complicated effects in his/her work. It may also serve as a reference book for advanced graduate courses in nonsmooth modelling, optimization and engineering. ... The book appears very attractive and it is certainly unique ...'
Daniel Goeleven in Mathematical Reviews, Issue 97h:49001

From the Publisher