Nonsmooth Vector Functions And Continuous Optimization

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Nonsmooth Vector Functions And Continuous Optimization

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Author : V. Jeyakumar
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-10-23

Nonsmooth Vector Functions And Continuous Optimization written by V. Jeyakumar 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 2007-10-23 with Mathematics categories.

Focusing on the study of nonsmooth vector functions, this book presents a comprehensive account of the calculus of generalized Jacobian matrices and their applications to continuous nonsmooth optimization problems, as well as variational inequalities in finite dimensions. The treatment is motivated by a desire to expose an elementary approach to nonsmooth calculus, using a set of matrices to replace the nonexistent Jacobian matrix of a continuous vector function.

Notfallmedizin

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Author : Friedrich W. Ahnefeld
language : en
Publisher:
Release Date : 1990

Notfallmedizin written by Friedrich W. Ahnefeld and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with Notfallmedizin categories.

Continuous Optimization And Variational Inequalities

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Author : Anurag Jayswal
language : en
Publisher: CRC Press
Release Date : 2022-09-13

Continuous Optimization And Variational Inequalities written by Anurag Jayswal and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-09-13 with Technology & Engineering categories.

The proposed book provides a comprehensive coverage of theory and methods in the areas of continuous optimization and variational inequality. It describes theory and solution methods for optimization with smooth and non-smooth functions, for variational inequalities with single-valued and multivalued mappings, and for related classes such as mixed variational inequalities, complementarity problems, and general equilibrium problems. The emphasis is made on revealing generic properties of these problems that allow creation of efficient solution methods. Salient Features The book presents a deep, wide-ranging introduction to the theory of the optimal control of processes governed by optimization techniques and variational inequality Several solution methods are provided which will help the reader to develop various optimization tools for real-life problems which can be modeled by optimization techniques involving linear and nonlinear functions. The book focuses on most recent contributions in the nonlinear phenomena, which can appear in various areas of human activities. This book also presents relevant mathematics clearly and simply to help solve real life problems in diverse fields such as mechanical engineering, management, control behavior, traffic signal, industry, etc. This book is aimed primarily at advanced undergraduates and graduate students pursuing computer engineering and electrical engineering courses. Researchers, academicians and industry people will also find this book useful.

System Modeling And Optimization

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Author : Adam Korytowski
language : en
Publisher: Springer
Release Date : 2009-10-27

System Modeling And Optimization written by Adam Korytowski and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-10-27 with Technology & Engineering categories.

rd This book constitutes a collection of extended versions of papers presented at the 23 IFIP TC7 Conference on System Modeling and Optimization, which was held in C- cow, Poland, on July 23–27, 2007. It contains 7 plenary and 22 contributed articles, the latter selected via a peer reviewing process. Most of the papers are concerned with optimization and optimal control. Some of them deal with practical issues, e. g. , p- formance-based design for seismic risk reduction, or evolutionary optimization in structural engineering. Many contributions concern optimization of infini- dimensional systems, ranging from a general overview of the variational analysis, through optimization and sensitivity analysis of PDE systems, to optimal control of neutral systems. A significant group of papers is devoted to shape analysis and opti- zation. Sufficient optimality conditions for ODE problems, and stochastic control methods applied to mathematical finance, are also investigated. The remaining papers are on mathematical programming, modeling, and information technology. The conference was the 23rd event in the series of such meetings biennially org- ized under the auspices of the Seventh Technical Committee “Systems Modeling and Optimization” of the International Federation for Information Processing (IFIP TC7).

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.

Second Order Variational Analysis In Optimization Variational Stability And Control

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Author : Boris S. Mordukhovich
language : en
Publisher: Springer Nature
Release Date : 2024-05-21

Second Order Variational Analysis In Optimization Variational Stability And Control 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 2024-05-21 with Mathematics categories.

This fundamental work is a sequel to monographs by the same author: Variational Analysis and Applications (2018) and the two Grundlehren volumes Variational Analysis and Generalized Differentiation: I Basic Theory, II Applications (2006). This present book is the first entirely devoted to second-order variational analysis with numerical algorithms and applications to practical models. It covers a wide range of topics including theoretical, numerical, and implementations that will interest researchers in analysis, applied mathematics, mathematical economics, engineering, and optimization. Inclusion of a variety of exercises and commentaries in each chapter allows the book to be used effectively in a course on this subject. This area has been well recognized as an important and rapidly developing area of nonlinear analysis and optimization with numerous applications. Consisting of 9 interrelated chapters, the book is self-contained with the inclusion of some preliminaries in Chapter 1. Results presented are useful tools for characterizations of fundamental notions of variational stability of solutions for diverse classes of problems in optimization and optimal control, the study of variational convexity of extended-real-valued functions and their specifications and variational sufficiency in optimization. Explicit calculations and important applications of second-order subdifferentials associated with the achieved characterizations of variational stability and related concepts, to the design and justification of second-order numerical algorithms for solving various classes of optimization problems, nonsmooth equations, and subgradient systems, are included. Generalized Newtonian algorithms are presented that show local and global convergence with linear, superlinear, and quadratic convergence rates. Algorithms are implemented to address interesting practical problems from the fields of machine learning, statistics, imaging, and other areas.

Optimization And Nonsmooth Analysis

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Author : Frank H. Clarke
language : en
Publisher: SIAM
Release Date : 1990-01-01

Optimization And Nonsmooth Analysis written by Frank H. Clarke and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990-01-01 with Mathematics categories.

This book has appeared in Russian translation and has been praised both for its lively exposition and its fundamental contributions. The author first develops a general theory of nonsmooth analysis and geometry which, together with a set of associated techniques, has had a profound effect on several branches of analysis and optimization. Clarke then applies these methods to obtain a powerful, unified approach to the analysis of problems in optimal control and mathematical programming. Examples are drawn from economics, engineering, mathematical physics, and various branches of analysis in this reprint volume.

Calculus Without Derivatives

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Author : Jean-Paul Penot
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-11-09

Calculus Without Derivatives written by Jean-Paul Penot 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 2012-11-09 with Mathematics categories.

Calculus Without Derivatives expounds the foundations and recent advances in nonsmooth analysis, a powerful compound of mathematical tools that obviates the usual smoothness assumptions. This textbook also provides significant tools and methods towards applications, in particular optimization problems. Whereas most books on this subject focus on a particular theory, this text takes a general approach including all main theories. In order to be self-contained, the book includes three chapters of preliminary material, each of which can be used as an independent course if needed. The first chapter deals with metric properties, variational principles, decrease principles, methods of error bounds, calmness and metric regularity. The second one presents the classical tools of differential calculus and includes a section about the calculus of variations. The third contains a clear exposition of convex analysis.

Nonsmooth Optimization Analysis And Algorithms With Applications To Optimal Control

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Author : Marko M Makela
language : en
Publisher: World Scientific
Release Date : 1992-05-07

Nonsmooth Optimization Analysis And Algorithms With Applications To Optimal Control written by Marko M Makela and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-05-07 with Mathematics categories.

This book is a self-contained elementary study for nonsmooth analysis and optimization, and their use in solution of nonsmooth optimal control problems. The first part of the book is concerned with nonsmooth differential calculus containing necessary tools for nonsmooth optimization. The second part is devoted to the methods of nonsmooth optimization and their development. A proximal bundle method for nonsmooth nonconvex optimization subject to nonsmooth constraints is constructed. In the last part nonsmooth optimization is applied to problems arising from optimal control of systems covered by partial differential equations. Several practical problems, like process control and optimal shape design problems are considered.

Methods Of Nonsmooth Optimization In Stochastic Programming

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Author : Wim Stefanus van Ackooij
language : en
Publisher: Springer Nature
Release Date : 2025-05-05

Methods Of Nonsmooth Optimization In Stochastic Programming written by Wim Stefanus van Ackooij and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-05-05 with Business & Economics categories.

This book presents a comprehensive series of methods in nonsmooth optimization, with a particular focus on their application in stochastic programming and dedicated algorithms for decision-making under uncertainty. Each method is accompanied by rigorous mathematical analysis, ensuring a deep understanding of the underlying principles. The theoretical discussions included are essential for comprehending the mechanics of various algorithms and the nature of the solutions they provide—whether they are global, local, stationary, or critical. The book begins by introducing fundamental tools from set-valued analysis, optimization, and probability theory. It then transitions from deterministic to stochastic optimization, starting with a thorough discussion of modeling, understanding uncertainty, and incorporating it into optimization problems. Following this foundation, the book explores numerical algorithms for nonsmooth optimization, covering well-known decomposition techniques and algorithms for convex optimization, mixed-integer convex programming, and nonconvex optimization. Additionally, it introduces numerical algorithms specifically for stochastic programming, focusing on stochastic programming with recourse, chance-constrained optimization, and detailed algorithms for both risk-neutral and risk-averse multistage stochastic programs. The book guides readers through the entire process, from defining optimization models for practical problems to presenting implementable algorithms that can be applied in practice. It is intended for students, practitioners, and scholars who may be unfamiliar with stochastic programming and nonsmooth optimization. The analyses provided are also valuable for practitioners who may not be interested in convergence proofs but wish to understand the nature of the solutions obtained.