One-dimensional Variational Problems

One-dimensional Variational Problems
Author: Giuseppe Buttazzo
Publisher: Oxford University Press
Total Pages: 282
Release: 1998
Genre: Mathematics
ISBN: 9780198504658

While easier to solve and accessible to a broader range of students, one-dimensional variational problems and their associated differential equations exhibit many of the same complex behavior of higher-dimensional problems. This book, the first moden introduction, emphasizes direct methods and provides an exceptionally clear view of the underlying theory.

Convex Analysis and Variational Problems

Convex Analysis and Variational Problems
Author: Ivar Ekeland
Publisher: SIAM
Total Pages: 414
Release: 1999-12-01
Genre: Mathematics
ISBN: 9781611971088

This book contains different developments of infinite dimensional convex programming in the context of convex analysis, including duality, minmax and Lagrangians, and convexification of nonconvex optimization problems in the calculus of variations (infinite dimension). It also includes the theory of convex duality applied to partial differential equations; no other reference presents this in a systematic way. The minmax theorems contained in this book have many useful applications, in particular the robust control of partial differential equations in finite time horizon. First published in English in 1976, this SIAM Classics in Applied Mathematics edition contains the original text along with a new preface and some additional references.

Calculus of Variations

Calculus of Variations
Author: Hansjörg Kielhöfer
Publisher: Springer
Total Pages: 242
Release: 2018-01-25
Genre: Mathematics
ISBN: 3319711237

This clear and concise textbook provides a rigorous introduction to the calculus of variations, depending on functions of one variable and their first derivatives. It is based on a translation of a German edition of the book Variationsrechnung (Vieweg+Teubner Verlag, 2010), translated and updated by the author himself. Topics include: the Euler-Lagrange equation for one-dimensional variational problems, with and without constraints, as well as an introduction to the direct methods. The book targets students who have a solid background in calculus and linear algebra, not necessarily in functional analysis. Some advanced mathematical tools, possibly not familiar to the reader, are given along with proofs in the appendix. Numerous figures, advanced problems and proofs, examples, and exercises with solutions accompany the book, making it suitable for self-study. The book will be particularly useful for beginning graduate students from the physical, engineering, and mathematical sciences with a rigorous theoretical background.

Branching Solutions To One-dimensional Variational Problems

Branching Solutions To One-dimensional Variational Problems
Author: Alexandr Ivanov
Publisher: World Scientific
Total Pages: 365
Release: 2001-01-17
Genre: Mathematics
ISBN: 981449433X

This book deals with the new class of one-dimensional variational problems — the problems with branching solutions. Instead of extreme curves (mappings of a segment to a manifold) we investigate extreme networks, which are mappings of graphs (one-dimensional cell complexes) to a manifold. Various applications of the approach are presented, such as several generalizations of the famous Steiner problem of finding the shortest network spanning given points of the plane.

Branching Solutions to One-dimensional Variational Problems

Branching Solutions to One-dimensional Variational Problems
Author: Alexander O. Ivanov
Publisher: World Scientific
Total Pages: 365
Release: 2001
Genre: Mathematics
ISBN: 9812810714

This book deals with the new class of one-dimensional variational problems OCo the problems with branching solutions. Instead of extreme curves (mappings of a segment to a manifold) we investigate extreme networks, which are mappings of graphs (one-dimensional cell complexes) to a manifold. Various applications of the approach are presented, such as several generalizations of the famous Steiner problem of finding the shortest network spanning given points of the plane. Contents: Preliminary Results; Networks Extremality Criteria; Linear Networks in R N; Extremals of Length Type Functionals: The Case of Parametric Networks; Extremals of Functionals Generated by Norms. Readership: Researchers in differential geometry and topology."

Mechanics and Thermodynamics of Continua

Mechanics and Thermodynamics of Continua
Author: Hershel Markovitz
Publisher: Springer Science & Business Media
Total Pages: 575
Release: 2012-12-06
Genre: Technology & Engineering
ISBN: 3642759750

Reprinted from Archive for Rational Mechanics and Analysis edited by C. Truesdell

Variational Analysis

Variational Analysis
Author: R. Tyrrell Rockafellar
Publisher: Springer Science & Business Media
Total Pages: 747
Release: 2009-06-26
Genre: Mathematics
ISBN: 3642024319

From its origins in the minimization of integral functionals, the notion of variations has evolved greatly in connection with applications in optimization, equilibrium, and control. This book develops a unified framework and provides a detailed exposition of variational geometry and subdifferential calculus in their current forms beyond classical and convex analysis. Also covered are set-convergence, set-valued mappings, epi-convergence, duality, and normal integrands.

Variational Methods for Structural Optimization

Variational Methods for Structural Optimization
Author: Andrej Cherkaev
Publisher: Springer Science & Business Media
Total Pages: 561
Release: 2012-12-06
Genre: Science
ISBN: 1461211883

This book bridges a gap between a rigorous mathematical approach to variational problems and the practical use of algorithms of structural optimization in engineering applications. The foundations of structural optimization are presented in sufficiently simple form as to make them available for practical use.

Calculus of Variations I

Calculus of Variations I
Author: Mariano Giaquinta
Publisher: Springer Science & Business Media
Total Pages: 498
Release: 2013-03-09
Genre: Mathematics
ISBN: 3662032783

This two-volume treatise is a standard reference in the field. It pays special attention to the historical aspects and the origins partly in applied problems—such as those of geometric optics—of parts of the theory. It contains an introduction to each chapter, section, and subsection and an overview of the relevant literature in the footnotes and bibliography. It also includes an index of the examples used throughout the book.

Finite-Dimensional Variational Inequalities and Complementarity Problems

Finite-Dimensional Variational Inequalities and Complementarity Problems
Author: Francisco Facchinei
Publisher: Springer Science & Business Media
Total Pages: 724
Release: 2007-06-14
Genre: Mathematics
ISBN: 0387218149

This is part one of a two-volume work presenting a comprehensive treatment of the finite-dimensional variational inequality and complementarity problem. It covers the basic theory of finite dimensional variational inequalities and complementarity problems. Coverage includes abundant exercises as well as an extensive bibliography. The book will be an enduring reference on the subject and provide the foundation for its sustained growth.