Variational Methods In Optimization
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Variational Methods In Optimization
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Author : Donald R. Smith
language : en
Publisher: Courier Corporation
Release Date : 1998-01-01
Variational Methods In Optimization written by Donald R. Smith and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-01-01 with Mathematics categories.
Highly readable text elucidates applications of the chain rule of differentiation, integration by parts, parametric curves, line integrals, double integrals, and elementary differential equations. 1974 edition.
Variational Methods In Shape Optimization Problems
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Author : Dorin Bucur
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-09-13
Variational Methods In Shape Optimization Problems written by Dorin Bucur and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-09-13 with Mathematics categories.
Shape optimization problems are treated from the classical and modern perspectives Targets a broad audience of graduate students in pure and applied mathematics, as well as engineers requiring a solid mathematical basis for the solution of practical problems Requires only a standard knowledge in the calculus of variations, differential equations, and functional analysis Driven by several good examples and illustrations Poses some open questions.
Variational Methods In Partially Ordered Spaces
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Author : Alfred Göpfert
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-04-18
Variational Methods In Partially Ordered Spaces written by Alfred Göpfert and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-04-18 with Business & Economics categories.
This book discusses basic tools of partially ordered spaces and applies them to variational methods in Nonlinear Analysis and for optimizing problems. This book is aimed at graduate students and research mathematicians.
Variational Methods In Nonlinear Analysis
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Author : Dimitrios C. Kravvaritis
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2020-04-06
Variational Methods In Nonlinear Analysis written by Dimitrios C. Kravvaritis and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-04-06 with Mathematics categories.
This well-thought-out book covers the fundamentals of nonlinear analysis, with a particular focus on variational methods and their applications. Starting from preliminaries in functional analysis, it expands in several directions such as Banach spaces, fixed point theory, nonsmooth analysis, minimax theory, variational calculus and inequalities, critical point theory, monotone, maximal monotone and pseudomonotone operators, and evolution problems.
Semismooth Newton Methods For Variational Inequalities And Constrained Optimization Problems In Function Spaces
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Author : Michael Ulbrich
language : en
Publisher: SIAM
Release Date : 2011-01-01
Semismooth Newton Methods For Variational Inequalities And Constrained Optimization Problems In Function Spaces written by Michael Ulbrich and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-01-01 with Mathematics categories.
Semismooth Newton methods are a modern class of remarkably powerful and versatile algorithms for solving constrained optimization problems with partial differential equations (PDEs), variational inequalities, and related problems. This book provides a comprehensive presentation of these methods in function spaces, striking a balance between thoroughly developed theory and numerical applications. Although largely self-contained, the book also covers recent developments in the field, such as state-constrained problems, and offers new material on topics such as improved mesh independence results. The theory and methods are applied to a range of practically important problems, including: optimal control of nonlinear elliptic differential equations, obstacle problems, and flow control of instationary Navier-Stokes fluids. In addition, the author covers adjoint-based derivative computation and the efficient solution of Newton systems by multigrid and preconditioned iterative methods.
Lagrange Multiplier Approach To Variational Problems And Applications
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Author : Kazufumi Ito
language : en
Publisher: SIAM
Release Date : 2008-01-01
Lagrange Multiplier Approach To Variational Problems And Applications written by Kazufumi Ito and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-01-01 with Mathematics categories.
Lagrange multiplier theory provides a tool for the analysis of a general class of nonlinear variational problems and is the basis for developing efficient and powerful iterative methods for solving these problems. This comprehensive monograph analyzes Lagrange multiplier theory and shows its impact on the development of numerical algorithms for problems posed in a function space setting. The authors develop and analyze efficient algorithms for constrained optimization and convex optimization problems based on the augumented Lagrangian concept and cover such topics as sensitivity analysis, convex optimization, second order methods, and shape sensitivity calculus. General theory is applied to challenging problems in optimal control of partial differential equations, image analysis, mechanical contact and friction problems, and American options for the Black-Scholes model.
Variational Calculus And Optimal Control
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Author : John L. Troutman
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Variational Calculus And Optimal Control written by John L. Troutman and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Although the calculus of variations has ancient origins in questions of Ar istotle and Zenodoros, its mathematical principles first emerged in the post calculus investigations of Newton, the Bernoullis, Euler, and Lagrange. Its results now supply fundamental tools of exploration to both mathematicians and those in the applied sciences. (Indeed, the macroscopic statements ob tained through variational principles may provide the only valid mathemati cal formulations of many physical laws. ) Because of its classical origins, variational calculus retains the spirit of natural philosophy common to most mathematical investigations prior to this century. The original applications, including the Bernoulli problem of finding the brachistochrone, require opti mizing (maximizing or minimizing) the mass, force, time, or energy of some physical system under various constraints. The solutions to these problems satisfy related differential equations discovered by Euler and Lagrange, and the variational principles of mechanics (especially that of Hamilton from the last century) show the importance of also considering solutions that just provide stationary behavior for some measure of performance of the system. However, many recent applications do involve optimization, in particular, those concerned with problems in optimal control. Optimal control is the rapidly expanding field developed during the last half-century to analyze optimal behavior of a constrained process that evolves in time according to prescribed laws. Its applications now embrace a variety of new disciplines, including economics and production planning.
Techniques Of Variational Analysis
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Author : Jonathan Borwein
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-06-18
Techniques Of Variational Analysis written by Jonathan Borwein and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-06-18 with Mathematics categories.
Borwein is an authority in the area of mathematical optimization, and his book makes an important contribution to variational analysis Provides a good introduction to the topic
Variational Analysis
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Author : R. Tyrrell Rockafellar
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-06-26
Variational Analysis written by R. Tyrrell Rockafellar and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-06-26 with Mathematics categories.
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. It refers not only to constrained movement away from a point, but also to modes of perturbation and approximation that are best describable by 'set convergence', variational convergence of functions and the like. This book develops a unified framework and, in finite dimension, 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, maximal monotone mappings, second-order subderivatives, measurable selections and normal integrands. The changes in this 3rd printing mainly concern various typographical corrections, and reference omissions that came to light in the previous printings. Many of these reached the authors' notice through their own re-reading, that of their students and a number of colleagues mentioned in the Preface. The authors also included a few telling examples as well as improved a few statements, with slightly weaker assumptions or have strengthened the conclusions in a couple of instances.
Duality In Optimization And Variational Inequalities
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Author : C.j. Goh
language : en
Publisher: CRC Press
Release Date : 2002-05-10
Duality In Optimization And Variational Inequalities written by C.j. Goh and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-05-10 with Mathematics categories.
This comprehensive volume covers a wide range of duality topics ranging from simple ideas in network flows to complex issues in non-convex optimization and multicriteria problems. In addition, it examines duality in the context of variational inequalities and vector variational inequalities, as generalizations to optimization. Duality in Optimizati