Optimization With Multivalued Mappings
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Optimization With Multivalued Mappings
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Author : Stephan Dempe
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-09-19
Optimization With Multivalued Mappings written by Stephan Dempe 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 2006-09-19 with Mathematics categories.
In the field of nondifferentiable nonconvex optimization, one of the most intensely investigated areas is that of optimization problems involving multivalued mappings in constraints or as the objective function. This book focuses on the tremendous development in the field that has taken place since the publication of the most recent volumes on the subject. The new topics studied include the formulation of optimality conditions using different kinds of generalized derivatives for set-valued mappings (such as, for example, the coderivative of Mordukhovich), the opening of new applications (e.g., the calibration of water supply systems), or the elaboration of new solution algorithms (e.g., smoothing methods). The book is divided into three parts. The focus in the first part is on bilevel programming. The chapters in the second part contain investigations of mathematical programs with equilibrium constraints. The third part is on multivalued set-valued optimization. The chapters were written by outstanding experts in the areas of bilevel programming, mathematical programs with equilibrium (or complementarity) constraints (MPEC), and set-valued optimization problems.
Optimization With Multivalued Mappings
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Author : Shōjirō Tagawa
language : en
Publisher:
Release Date : 1979
Optimization With Multivalued Mappings written by Shōjirō Tagawa and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1979 with categories.
Approximation And Optimization Of Discrete And Differential Inclusions
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Author : Elimhan N Mahmudov
language : en
Publisher: Elsevier
Release Date : 2011-08-25
Approximation And Optimization Of Discrete And Differential Inclusions written by Elimhan N Mahmudov and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-08-25 with Mathematics categories.
Optimal control theory has numerous applications in both science and engineering. This book presents basic concepts and principles of mathematical programming in terms of set-valued analysis and develops a comprehensive optimality theory of problems described by ordinary and partial differential inclusions. In addition to including well-recognized results of variational analysis and optimization, the book includes a number of new and important ones Includes practical examples
Nonsmooth Equations In Optimization
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Author : Diethard Klatte
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-12-17
Nonsmooth Equations In Optimization written by Diethard Klatte 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 2005-12-17 with Mathematics categories.
Many questions dealing with solvability, stability and solution methods for va- ational inequalities or equilibrium, optimization and complementarity problems lead to the analysis of certain (perturbed) equations. This often requires a - formulation of the initial model being under consideration. Due to the specific of the original problem, the resulting equation is usually either not differ- tiable (even if the data of the original model are smooth), or it does not satisfy the assumptions of the classical implicit function theorem. This phenomenon is the main reason why a considerable analytical inst- ment dealing with generalized equations (i.e., with finding zeros of multivalued mappings) and nonsmooth equations (i.e., the defining functions are not c- tinuously differentiable) has been developed during the last 20 years, and that under very different viewpoints and assumptions. In this theory, the classical hypotheses of convex analysis, in particular, monotonicity and convexity, have been weakened or dropped, and the scope of possible applications seems to be quite large. Briefly, this discipline is often called nonsmooth analysis, sometimes also variational analysis. Our book fits into this discipline, however, our main intention is to develop the analytical theory in close connection with the needs of applications in optimization and related subjects. Main Topics of the Book 1. Extended analysis of Lipschitz functions and their generalized derivatives, including ”Newton maps” and regularity of multivalued mappings. 2. Principle of successive approximation under metric regularity and its - plication to implicit functions.
Topological Fixed Point Theory Of Multivalued Mappings
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Author : Lech Górniewicz
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-06-03
Topological Fixed Point Theory Of Multivalued Mappings written by Lech Górniewicz 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 2006-06-03 with Mathematics categories.
This book is devoted to the topological fixed point theory of multivalued mappings including applications to differential inclusions and mathematical economy. It is the first monograph dealing with the fixed point theory of multivalued mappings in metric ANR spaces. Although the theoretical material was tendentiously selected with respect to applications, the text is self-contained. Current results are presented.
Multivalued Analysis And Nonlinear Programming Problems With Perturbations
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Author : B. Luderer
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Multivalued Analysis And Nonlinear Programming Problems With Perturbations written by B. Luderer 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 2013-03-09 with Mathematics categories.
The book presents a treatment of topological and differential properties of multivalued mappings and marginal functions. In addition, applications to sensitivity analysis of nonlinear programming problems under perturbations are studied. Properties of marginal functions associated with optimization problems are analyzed under quite general constraints defined by means of multivalued mappings. A unified approach to directional differentiability of functions and multifunctions forms the base of the volume. Nonlinear programming problems involving quasidifferentiable functions are considered as well. A significant part of the results are based on theories and concepts of two former Soviet Union researchers, Demyanov and Rubinov, and have never been published in English before. It contains all the necessary information from multivalued analysis and does not require special knowledge, but assumes basic knowledge of calculus at an undergraduate level.
Optimization Algorithms
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Author : Jan Valdman
language : en
Publisher: BoD – Books on Demand
Release Date : 2018-09-05
Optimization Algorithms written by Jan Valdman and has been published by BoD – Books on Demand this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-09-05 with Mathematics categories.
This book presents examples of modern optimization algorithms. The focus is on a clear understanding of underlying studied problems, understanding described algorithms by a broad range of scientists and providing (computational) examples that a reader can easily repeat.
Optimization With Pde Constraints
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Author : Ronald Hoppe
language : en
Publisher: Springer
Release Date : 2014-09-11
Optimization With Pde Constraints written by Ronald Hoppe and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-11 with Computers categories.
This book on PDE Constrained Optimization contains contributions on the mathematical analysis and numerical solution of constrained optimal control and optimization problems where a partial differential equation (PDE) or a system of PDEs appears as an essential part of the constraints. The appropriate treatment of such problems requires a fundamental understanding of the subtle interplay between optimization in function spaces and numerical discretization techniques and relies on advanced methodologies from the theory of PDEs and numerical analysis as well as scientific computing. The contributions reflect the work of the European Science Foundation Networking Programme ’Optimization with PDEs’ (OPTPDE).
Bilevel Optimization
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Author : Stephan Dempe
language : en
Publisher: Springer Nature
Release Date : 2020-11-23
Bilevel Optimization written by Stephan Dempe and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-11-23 with Business & Economics categories.
2019 marked the 85th anniversary of Heinrich Freiherr von Stackelberg’s habilitation thesis “Marktform und Gleichgewicht,” which formed the roots of bilevel optimization. Research on the topic has grown tremendously since its introduction in the field of mathematical optimization. Besides the substantial advances that have been made from the perspective of game theory, many sub-fields of bilevel optimization have emerged concerning optimal control, multiobjective optimization, energy and electricity markets, management science, security and many more. Each chapter of this book covers a specific aspect of bilevel optimization that has grown significantly or holds great potential to grow, and was written by top experts in the corresponding area. In other words, unlike other works on the subject, this book consists of surveys of different topics on bilevel optimization. Hence, it can serve as a point of departure for students and researchers beginning their research journey or pursuing related projects. It also provides a unique opportunity for experienced researchers in the field to learn about the progress made so far and directions that warrant further investigation. All chapters have been peer-reviewed by experts on mathematical optimization.
Variational Analysis And Generalized Differentiation In Optimization And Control
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Author : Regina S. Burachik
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-11-25
Variational Analysis And Generalized Differentiation In Optimization And Control written by Regina S. Burachik 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 2010-11-25 with Mathematics categories.
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.