Nonsmooth Vector Functions and Continuous Optimization PDF Download
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Author: V. Jeyakumar
Publisher: Springer Science & Business Media
ISBN: 0387737170
Category : Mathematics
Languages : en
Pages : 277
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Book Description
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.
Author: V. Jeyakumar
Publisher: Springer Science & Business Media
ISBN: 0387737170
Category : Mathematics
Languages : en
Pages : 277
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Book Description
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.
Author: Friedrich W. Ahnefeld
Publisher:
ISBN: 9780387520278
Category : Notfallmedizin
Languages : en
Pages : 385
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Book Description
Author: Marko M Makela
Publisher: World Scientific
ISBN: 9814522414
Category : Mathematics
Languages : en
Pages : 268
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Book Description
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.
Author: Anurag Jayswal
Publisher: CRC Press
ISBN: 1000648931
Category : Technology & Engineering
Languages : en
Pages : 379
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Book Description
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.
Author: Adam Korytowski
Publisher: Springer
ISBN: 3642048021
Category : Technology & Engineering
Languages : en
Pages : 515
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Book Description
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).
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: Boris S. Mordukhovich
Publisher: Springer Nature
ISBN: 303153476X
Category :
Languages : en
Pages : 802
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Book Description
Author: Adil Bagirov
Publisher: Springer
ISBN: 3319081144
Category : Business & Economics
Languages : en
Pages : 377
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Book Description
This book is the first easy-to-read text on nonsmooth optimization (NSO, not necessarily differentiable optimization). Solving these kinds of problems plays a critical role in many industrial applications and real-world modeling systems, for example in the context of image denoising, optimal control, neural network training, data mining, economics and computational chemistry and physics. The book covers both the theory and the numerical methods used in NSO and provide an overview of different problems arising in the field. It is organized into three parts: 1. convex and nonconvex analysis and the theory of NSO; 2. test problems and practical applications; 3. a guide to NSO software. The book is ideal for anyone teaching or attending NSO courses. As an accessible introduction to the field, it is also well suited as an independent learning guide for practitioners already familiar with the basics of optimization.
Author: Frank H. Clarke
Publisher: SIAM
ISBN: 0898712564
Category : Mathematics
Languages : en
Pages : 317
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Book Description
Mathematical Reviews said of this book that it was 'destined to become a classical reference.' 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.
Author: Claude Lemarechal
Publisher: Elsevier
ISBN: 1483188760
Category : Technology & Engineering
Languages : en
Pages : 195
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Book Description
Nonsmooth Optimization contains the proceedings of a workshop on non-smooth optimization (NSO) held from March 28 to April 8,1977 in Austria under the auspices of the International Institute for Applied Systems Analysis. The papers explore the techniques and theory of NSO and cover topics ranging from systems of inequalities to smooth approximation of non-smooth functions, as well as quadratic programming and line searches. Comprised of nine chapters, this volume begins with a survey of Soviet research on subgradient optimization carried out since 1962, followed by a discussion on rates of convergence in subgradient optimization. The reader is then introduced to the method of subgradient optimization in an abstract setting and the minimal hypotheses required to ensure convergence; NSO and nonlinear programming; and bundle methods in NSO. A feasible descent algorithm for linearly constrained least squares problems is described. The book also considers sufficient minimization of piecewise-linear univariate functions before concluding with a description of the method of parametric decomposition in mathematical programming. This monograph will be of interest to mathematicians and mathematics students.
