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This title in other editions

Other titles in the Springer Optimization and Its Applications series:

Springer Optimization and Its Applications #10: Nonsmooth Vector Functions and Continuous Optimization

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Springer Optimization and Its Applications #10: Nonsmooth Vector Functions and Continuous Optimization Cover

 

Synopses & Reviews

Publisher Comments:

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.

Synopsis:

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, as well as variational inequalities in finite dimensions. The treatment is motivated by a desire to expose an elementary approach to nonsmooth calculus, using a set of matrices to replace the nonexistent Jacobian matrix of a continuous vector function.

Table of Contents

Preface.- Pseudo-Jacobian Matrices.- Calculus Rules for Pseudo-Jacobians.- Openness of Continuous Vector Functions.- Nonsmooth Mathematical Programming Problems.- Monotone Operators and Nonsmooth Variational Inequalities.- Bibliographical Notes.- References.- Notations.- Index.

Product Details

ISBN:
9781441944726
Author:
Jeyakumar, V.
Publisher:
Springer
Author:
Luc, Dinh The
Location:
Boston, MA
Subject:
Linear Programming
Subject:
Calculus of Variations and Optimal Control; Optimization
Subject:
Operations Research, Mathematical Programming
Subject:
Operations Research/Decision Theory
Subject:
Appl.Mathematics/Computational Methods of Engineering
Subject:
Mathematical Modeling and Industrial Mathematics
Subject:
APPLICATIONS OF MATHEMATICS
Subject:
Operations Research, Management Science
Subject:
Applications of Mathematics <P>A recent significant innovation in mathematical sciences has been the progressive use of nonsmooth calculus as a key tool of modern analysis in many areas of mathematics, operations research, and engineering. Focusing on the
Subject:
Mathematics-Computer
Subject:
Calculus
Subject:
Operation Research/Decision Theory
Subject:
Mathematics
Subject:
B
Subject:
mathematics and statistics
Subject:
Mathematical optimization
Subject:
Operations Research
Subject:
Engineering mathematics
Copyright:
Edition Description:
Softcover reprint of hardcover 1st ed. 2008
Series:
Springer Optimization and Its Applications
Series Volume:
10
Publication Date:
20101129
Binding:
TRADE PAPER
Language:
English
Pages:
280
Dimensions:
235 x 155 mm 428 gr

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Springer Optimization and Its Applications #10: Nonsmooth Vector Functions and Continuous Optimization New Trade Paper
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$140.25 In Stock
Product details 280 pages Springer - English 9781441944726 Reviews:
"Synopsis" by , 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, as well as variational inequalities in finite dimensions. The treatment is motivated by a desire to expose an elementary approach to nonsmooth calculus, using a set of matrices to replace the nonexistent Jacobian matrix of a continuous vector function.
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