Techniques of Variational Analysis PDF Download
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Author: Jonathan Borwein
Publisher: Springer Science & Business Media
ISBN: 0387282718
Category : Mathematics
Languages : en
Pages : 368
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Book Description
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
Author: Jonathan Borwein
Publisher: Springer Science & Business Media
ISBN: 0387282718
Category : Mathematics
Languages : en
Pages : 368
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Book Description
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
Author: R. Tyrrell Rockafellar
Publisher: Springer Science & Business Media
ISBN: 3642024319
Category : Mathematics
Languages : en
Pages : 747
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Book Description
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.
Author: Dimitrios C. Kravvaritis
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110647451
Category : Mathematics
Languages : en
Pages : 384
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Book Description
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.
Author: Georg Dolzmann
Publisher: Springer Science & Business Media
ISBN: 9783540001140
Category : Mathematics
Languages : en
Pages : 228
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Book Description
Phase transformations in solids typically lead to surprising mechanical behaviour with far reaching technological applications. The mathematical modeling of these transformations in the late 80s initiated a new field of research in applied mathematics, often referred to as mathematical materials science, with deep connections to the calculus of variations and the theory of partial differential equations. This volume gives a brief introduction to the essential physical background, in particular for shape memory alloys and a special class of polymers (nematic elastomers). Then the underlying mathematical concepts are presented with a strong emphasis on the importance of quasiconvex hulls of sets for experiments, analytical approaches, and numerical simulations.
Author: Donald R. Smith
Publisher: Courier Corporation
ISBN: 9780486404554
Category : Mathematics
Languages : en
Pages : 406
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Book Description
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.
Author: Boris S. Mordukhovich
Publisher: Springer Science & Business Media
ISBN: 3540312471
Category : Mathematics
Languages : en
Pages : 598
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Book Description
Comprehensive and state-of-the art study of the basic concepts and principles of variational analysis and generalized differentiation in both finite-dimensional and infinite-dimensional spaces Presents numerous applications to problems in the optimization, equilibria, stability and sensitivity, control theory, economics, mechanics, etc.
Author: Boris S. Mordukhovich
Publisher: Springer Science & Business Media
ISBN: 3540312463
Category : Mathematics
Languages : en
Pages : 630
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Book Description
Comprehensive and state-of-the art study of the basic concepts and principles of variational analysis and generalized differentiation in both finite-dimensional and infinite-dimensional spaces Presents numerous applications to problems in the optimization, equilibria, stability and sensitivity, control theory, economics, mechanics, etc.
Author: Regina S. Burachik
Publisher: Springer Science & Business Media
ISBN: 1441904379
Category : Mathematics
Languages : en
Pages : 237
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Book Description
This book presents some 20 papers describing recent developments in advanced variational analysis, optimization, and control systems, especially those based on modern variational techniques and tools of generalized differentiation.
Author: Akhtar A. Khan
Publisher: CRC Press
ISBN: 1351712071
Category : Business & Economics
Languages : en
Pages : 324
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Book Description
This book contains the latest advances in variational analysis and set / vector optimization, including uncertain optimization, optimal control and bilevel optimization. Recent developments concerning scalarization techniques, necessary and sufficient optimality conditions and duality statements are given. New numerical methods for efficiently solving set optimization problems are provided. Moreover, applications in economics, finance and risk theory are discussed. Summary The objective of this book is to present advances in different areas of variational analysis and set optimization, especially uncertain optimization, optimal control and bilevel optimization. Uncertain optimization problems will be approached from both a stochastic as well as a robust point of view. This leads to different interpretations of the solutions, which widens the choices for a decision-maker given his preferences. Recent developments regarding linear and nonlinear scalarization techniques with solid and nonsolid ordering cones for solving set optimization problems are discussed in this book. These results are useful for deriving optimality conditions for set and vector optimization problems. Consequently, necessary and sufficient optimality conditions are presented within this book, both in terms of scalarization as well as generalized derivatives. Moreover, an overview of existing duality statements and new duality assertions is given. The book also addresses the field of variable domination structures in vector and set optimization. Including variable ordering cones is especially important in applications such as medical image registration with uncertainties. This book covers a wide range of applications of set optimization. These range from finance, investment, insurance, control theory, economics to risk theory. As uncertain multi-objective optimization, especially robust approaches, lead to set optimization, one main focus of this book is uncertain optimization. Important recent developments concerning numerical methods for solving set optimization problems sufficiently fast are main features of this book. These are illustrated by various examples as well as easy-to-follow-steps in order to facilitate the decision process for users. Simple techniques aimed at practitioners working in the fields of mathematical programming, finance and portfolio selection are presented. These will help in the decision-making process, as well as give an overview of nondominated solutions to choose from.
Author: Asen L. Dontchev
Publisher: Springer Nature
ISBN: 3030799115
Category : Mathematics
Languages : en
Pages : 223
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Book Description
This book presents an introduction to variational analysis, a field which unifies theories and techniques developed in calculus of variations, optimization, and control, and covers convex analysis, nonsmooth analysis, and set-valued analysis. It focuses on problems with constraints, the analysis of which involves set-valued mappings and functions that are not differentiable. Applications of variational analysis are interdisciplinary, ranging from financial planning to steering a flying object. The book is addressed to graduate students, researchers, and practitioners in mathematical sciences, engineering, economics, and finance. A typical reader of the book should be familiar with multivariable calculus and linear algebra. Some basic knowledge in optimization, control, and elementary functional analysis is desirable, but all necessary background material is included in the book.
