Quasidifferentiability and Nonsmooth Modelling in Mechanics, Engineering and Economics
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...
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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. Booknews 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)
PrefaceIntroductionGuidelines for the Readers1Nonsmooth Analysis the One-dimensional Case12Quasidifferentiable Functions and Sets Quasidifferentiable Optimization and Optimality Conditions493Nonsmooth Mechanics I. Nonsmooth Modelling in Mechanics934Nonsmooth Mechanics II. Variational Formulations using Quasidifferentiability1395Additional Topics. Stability, Economics, Flow Problems, Dynamic Problems1776Nonsmooth Optimization Algorithms. Quasidifferentiable and Codifferentiable Optimization2057Nonsmooth Computational Mechanics I. Modelling and Applications2538Nonsmooth Computational Mechanics II. Algorithms and Examples297Subject Index345
\ BooknewsA 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)\ \
