Vector Optimization And Monotone Operators Via Convex Duality
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Vector Optimization And Monotone Operators Via Convex Duality
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Author : Sorin-Mihai Grad
language : en
Publisher: Springer
Release Date : 2014-09-03
Vector Optimization And Monotone Operators Via Convex Duality written by Sorin-Mihai Grad and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-03 with Business & Economics categories.
This book investigates several duality approaches for vector optimization problems, while also comparing them. Special attention is paid to duality for linear vector optimization problems, for which a vector dual that avoids the shortcomings of the classical ones is proposed. Moreover, the book addresses different efficiency concepts for vector optimization problems. Among the problems that appear when the framework is generalized by considering set-valued functions, an increasing interest is generated by those involving monotone operators, especially now that new methods for approaching them by means of convex analysis have been developed. Following this path, the book provides several results on different properties of sums of monotone operators.
Convex Optimization
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Author : Stephen P. Boyd
language : en
Publisher: Cambridge University Press
Release Date : 2004-03-08
Convex Optimization written by Stephen P. Boyd and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-03-08 with Business & Economics categories.
Convex optimization problems arise frequently in many different fields. This book provides a comprehensive introduction to the subject, and shows in detail how such problems can be solved numerically with great efficiency. The book begins with the basic elements of convex sets and functions, and then describes various classes of convex optimization problems. Duality and approximation techniques are then covered, as are statistical estimation techniques. Various geometrical problems are then presented, and there is detailed discussion of unconstrained and constrained minimization problems, and interior-point methods. The focus of the book is on recognizing convex optimization problems and then finding the most appropriate technique for solving them. It contains many worked examples and homework exercises and will appeal to students, researchers and practitioners in fields such as engineering, computer science, mathematics, statistics, finance and economics.
Convex Optimization Theory Algorithms And Applications
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Author : Balendu Bhooshan Upadhyay
language : en
Publisher: Springer Nature
Release Date : 2025-04-25
Convex Optimization Theory Algorithms And Applications written by Balendu Bhooshan Upadhyay and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-04-25 with Mathematics categories.
This volume includes chapters on topics presented at the conference on Recent Trends in Convex Optimization: Theory, Algorithms and Applications (RTCOTAA-2020), held at the Department of Mathematics, Indian Institute of Technology Patna, Bihar, India, from 29–31 October 2020. It discusses a comprehensive exploration of the realm of optimization, encompassing both the theoretical underpinnings and the multifaceted real-life implementations of the optimization theory. It meticulously features essential optimization concepts, such as convex analysis, generalized convexity, monotonicity, etc., elucidating their theoretical advancements and significance in the optimization sphere. Multiobjective optimization is a pivotal topic which addresses the inherent difficulties faced in conflicting objectives. The book delves into various theoretical concepts and covers some practical algorithmic approaches to solve multiobjective optimization, such as the line search and the enhanced non-monotone quasi-Newton algorithms. It also deliberates on several other significant topics in optimization, such as the perturbation approach for vector optimization, and solution methods for set-valued optimization. Nonsmooth optimization is extensively covered, with in-depth discussions on various well-known tools of nonsmooth analysis, such as convexificators, limiting subdifferentials, tangential subdifferentials, quasi-differentials, etc. Notable optimization algorithms, such as the interior point algorithm and Lemke’s algorithm, are dissected in detail, offering insights into their applicability and effectiveness. The book explores modern applications of optimization theory, for instance, optimized image encryption, resource allocation, target tracking problems, deep learning, entropy optimization, etc. Ranging from gradient-based optimization algorithms to metaheuristic approaches such as particle swarm optimization, the book navigates through the intersection of optimization theory and deep learning, thereby unravelling new research perspectives in artificial intelligence, machine learning and other fields of modern science. Designed primarily for graduate students and researchers across a variety of disciplines such as mathematics, operations research, electrical and electronics engineering, computer science, robotics, deep learning, image processing and artificial intelligence, this book serves as a comprehensive resource for someone interested in exploring the multifaceted domain of mathematical optimization and its myriad applications.
Splitting Algorithms Modern Operator Theory And Applications
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Author : Heinz H. Bauschke
language : en
Publisher: Springer Nature
Release Date : 2019-11-06
Splitting Algorithms Modern Operator Theory And Applications written by Heinz H. Bauschke and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-11-06 with Mathematics categories.
This book brings together research articles and state-of-the-art surveys in broad areas of optimization and numerical analysis with particular emphasis on algorithms. The discussion also focuses on advances in monotone operator theory and other topics from variational analysis and nonsmooth optimization, especially as they pertain to algorithms and concrete, implementable methods. The theory of monotone operators is a central framework for understanding and analyzing splitting algorithms. Topics discussed in the volume were presented at the interdisciplinary workshop titled Splitting Algorithms, Modern Operator Theory, and Applications held in Oaxaca, Mexico in September, 2017. Dedicated to Jonathan M. Borwein, one of the most versatile mathematicians in contemporary history, this compilation brings theory together with applications in novel and insightful ways.
Multi Composed Programming With Applications To Facility Location
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Author : Oleg Wilfer
language : en
Publisher: Springer Nature
Release Date : 2020-05-27
Multi Composed Programming With Applications To Facility Location written by Oleg Wilfer and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-05-27 with Mathematics categories.
Oleg Wilfer presents a new conjugate duality concept for geometric and cone constrained optimization problems whose objective functions are a composition of finitely many functions. As an application, the author derives results for single minmax location problems formulated by means of extended perturbed minimal time functions as well as for multi-facility minmax location problems defined by gauges. In addition, he provides formulae of projections onto the epigraphs of gauges to solve these kinds of location problems numerically by using parallel splitting algorithms. Numerical comparisons of recent methods show the excellent performance of the proposed solving technique. About the Author: Dr. Oleg Wilfer received his PhD at the Faculty of Mathematics of Chemnitz University of Technology, Germany. He is currently working as a development engineer in the automotive industry.
Convex Analysis And Beyond
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Author : Boris S. Mordukhovich
language : en
Publisher: Springer Nature
Release Date : 2022-04-24
Convex Analysis And Beyond written by Boris S. Mordukhovich and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-04-24 with Mathematics categories.
This book presents a unified theory of convex functions, sets, and set-valued mappings in topological vector spaces with its specifications to locally convex, Banach and finite-dimensional settings. These developments and expositions are based on the powerful geometric approach of variational analysis, which resides on set extremality with its characterizations and specifications in the presence of convexity. Using this approach, the text consolidates the device of fundamental facts of generalized differential calculus to obtain novel results for convex sets, functions, and set-valued mappings in finite and infinite dimensions. It also explores topics beyond convexity using the fundamental machinery of convex analysis to develop nonconvex generalized differentiation and its applications. The text utilizes an adaptable framework designed with researchers as well as multiple levels of students in mind. It includes many exercises and figures suited to graduate classes in mathematical sciences that are also accessible to advanced students in economics, engineering, and other applications. In addition, it includes chapters on convex analysis and optimization in finite-dimensional spaces that will be useful to upper undergraduate students, whereas the work as a whole provides an ample resource to mathematicians and applied scientists, particularly experts in convex and variational analysis, optimization, and their applications.
Operations Research Proceedings 2014
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Author : Marco Lübbecke
language : en
Publisher: Springer
Release Date : 2016-02-20
Operations Research Proceedings 2014 written by Marco Lübbecke and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-02-20 with Business & Economics categories.
This book contains a selection of refereed papers presented at the "International Conference on Operations Research (OR 2014)", which took place at RWTH Aachen University, Germany, September 2-5, 2014. More than 800 scientists and students from 47 countries attended OR 2014 and presented more than 500 papers in parallel topical streams, as well as special award sessions. The theme of the conference and its proceedings is "Business Analytics and Optimization".
Introduction To The Theory Of Nonlinear Optimization
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Author : Johannes Jahn
language : en
Publisher: Springer Nature
Release Date : 2020-07-02
Introduction To The Theory Of Nonlinear Optimization written by Johannes Jahn and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-07-02 with Business & Economics categories.
This book serves as an introductory text to optimization theory in normed spaces and covers all areas of nonlinear optimization. It presents fundamentals with particular emphasis on the application to problems in the calculus of variations, approximation and optimal control theory. The reader is expected to have a basic knowledge of linear functional analysis.
Convexity From The Geometric Point Of View
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Author : Vitor Balestro
language : en
Publisher: Springer Nature
Release Date : 2024-07-14
Convexity From The Geometric Point Of View written by Vitor Balestro and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-07-14 with Mathematics categories.
This text gives a comprehensive introduction to the “common core” of convex geometry. Basic concepts and tools which are present in all branches of that field are presented with a highly didactic approach. Mainly directed to graduate and advanced undergraduates, the book is self-contained in such a way that it can be read by anyone who has standard undergraduate knowledge of analysis and of linear algebra. Additionally, it can be used as a single reference for a complete introduction to convex geometry, and the content coverage is sufficiently broad that the reader may gain a glimpse of the entire breadth of the field and various subfields. The book is suitable as a primary text for courses in convex geometry and also in discrete geometry (including polytopes). It is also appropriate for survey type courses in Banach space theory, convex analysis, differential geometry, and applications of measure theory. Solutions to all exercises are available to instructors who adopt the text for coursework. Most chapters use the same structure with the first part presenting theory and the next containing a healthy range of exercises. Some of the exercises may even be considered as short introductions to ideas which are not covered in the theory portion. Each chapter has a notes section offering a rich narrative to accompany the theory, illuminating the development of ideas, and providing overviews to the literature concerning the covered topics. In most cases, these notes bring the reader to the research front. The text includes many figures that illustrate concepts and some parts of the proofs, enabling the reader to have a better understanding of the geometric meaning of the ideas. An appendix containing basic (and geometric) measure theory collects useful information for convex geometers.
Conjugate Duality And Optimization
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Author : R. Tyrrell Rockafellar
language : en
Publisher: SIAM
Release Date : 1974-01-01
Conjugate Duality And Optimization written by R. Tyrrell Rockafellar and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1974-01-01 with Technology & Engineering categories.
Provides a relatively brief introduction to conjugate duality in both finite- and infinite-dimensional problems. An emphasis is placed on the fundamental importance of the concepts of Lagrangian function, saddle-point, and saddle-value. General examples are drawn from nonlinear programming, approximation, stochastic programming, the calculus of variations, and optimal control.