Overview
- Based on major original contributions of the authors to the research area
- No other recent monograph in nonsmooth analysis is devoted to vector-valued maps, a growing area of research
Part of the book series: Springer Optimization and Its Applications (SOIA, volume 10)
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Table of contents (5 chapters)
Keywords
About this book
A recent significant innovation in mathematical sciences has been the progressive use of nonsmooth calculus, an extension of the differential calculus, as a key tool of modern analysis in many areas of mathematics, operations research, and engineering. Focusing on the study of nonsmooth vector functions, this book presents a comprehensive account of the calculus of generalized Jacobian matrices and their applications to continuous nonsmooth optimization problems and variational inequalities in finite dimensions.
The treatment is motivated by a desire to expose an elementary approach to nonsmooth calculus by using a set of matrices to replace the nonexistent Jacobian matrix of a continuous vector function. Such a set of matrices forms a new generalized Jacobian, called pseudo-Jacobian. A direct extension of the classical derivative that follows simple rules of calculus, the pseudo-Jacobian provides an axiomatic approach to nonsmooth calculus, a flexible tool for handling nonsmooth continuous optimization problems.
Illustrated by numerous examples of known generalized derivatives, the work may serve as a valuable reference for graduate students, researchers, and applied mathematicians who wish to use nonsmooth techniques and continuous optimization to model and solve problems in mathematical programming, operations research, and engineering. Readers require only a modest background in undergraduate mathematical analysis to follow the material with minimal effort.
Authors and Affiliations
Bibliographic Information
Book Title: Nonsmooth Vector Functions and Continuous Optimization
Authors: V. Jeyakumar, D.T. LUC
Series Title: Springer Optimization and Its Applications
DOI: https://doi.org/10.1007/978-0-387-73717-1
Publisher: Springer New York, NY
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag US 2008
Hardcover ISBN: 978-0-387-73716-4Published: 25 October 2007
Softcover ISBN: 978-1-4419-4472-6Published: 29 November 2010
eBook ISBN: 978-0-387-73717-1Published: 23 October 2007
Series ISSN: 1931-6828
Series E-ISSN: 1931-6836
Edition Number: 1
Number of Pages: X, 270
Topics: Calculus of Variations and Optimal Control; Optimization, Analysis, Optimization, Operations Research, Management Science, Operations Research/Decision Theory, Mathematical and Computational Engineering