Newton Type Methods For Optimization And Variational Problems

Author : Alexey F. Izmailov
Publisher : Springer
ISBN 13 : 3319042475
Total Pages : 587 pages
Book Rating : 4.73/5 ( download)

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Download or read book Newton-Type Methods for Optimization and Variational Problems written by Alexey F. Izmailov and published by Springer. This book was released on 2014-07-08 with total page 587 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents comprehensive state-of-the-art theoretical analysis of the fundamental Newtonian and Newtonian-related approaches to solving optimization and variational problems. A central focus is the relationship between the basic Newton scheme for a given problem and algorithms that also enjoy fast local convergence. The authors develop general perturbed Newtonian frameworks that preserve fast convergence and consider specific algorithms as particular cases within those frameworks, i.e., as perturbations of the associated basic Newton iterations. This approach yields a set of tools for the unified treatment of various algorithms, including some not of the Newton type per se. Among the new subjects addressed is the class of degenerate problems. In particular, the phenomenon of attraction of Newton iterates to critical Lagrange multipliers and its consequences as well as stabilized Newton methods for variational problems and stabilized sequential quadratic programming for optimization. This volume will be useful to researchers and graduate students in the fields of optimization and variational analysis.

Author : Michael Ulbrich
Publisher : SIAM
ISBN 13 : 9781611970692
Total Pages : 322 pages
Book Rating : 4.95/5 ( download)

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Download or read book Semismooth Newton Methods for Variational Inequalities and Constrained Optimization Problems in Function Spaces written by Michael Ulbrich and published by SIAM. This book was released on 2011-01-01 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: Semismooth Newton methods are a modern class of remarkably powerful and versatile algorithms for solving constrained optimization problems with partial differential equations (PDEs), variational inequalities, and related problems. This book provides a comprehensive presentation of these methods in function spaces, striking a balance between thoroughly developed theory and numerical applications. Although largely self-contained, the book also covers recent developments in the field, such as state-constrained problems, and offers new material on topics such as improved mesh independence results. The theory and methods are applied to a range of practically important problems, including: optimal control of nonlinear elliptic differential equations, obstacle problems, and flow control of instationary Navier-Stokes fluids. In addition, the author covers adjoint-based derivative computation and the efficient solution of Newton systems by multigrid and preconditioned iterative methods.

Author : Boris S. Mordukhovich
Publisher : Springer Nature
ISBN 13 : 303153476X
Total Pages : 802 pages
Book Rating : 4.68/5 ( download)

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Download or read book Second-Order Variational Analysis in Optimization, Variational Stability, and Control written by Boris S. Mordukhovich and published by Springer Nature. This book was released on with total page 802 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Ioannis K. Argyros
Publisher : Springer Science & Business Media
ISBN 13 : 0387727434
Total Pages : 513 pages
Book Rating : 4.31/5 ( download)

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Download or read book Convergence and Applications of Newton-type Iterations written by Ioannis K. Argyros and published by Springer Science & Business Media. This book was released on 2008-06-12 with total page 513 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is devoted to a comprehensive treatment of iterative methods for solving nonlinear equations with particular emphasis on semi-local convergence analysis. Theoretical results are applied to engineering, dynamic economic systems, input-output systems, nonlinear and linear differential equations, and optimization problems. Accompanied by many exercises, some with solutions, the book may be used as a supplementary text in the classroom for an advanced course on numerical functional analysis.

Author : Alexander J. Zaslavski
Publisher : Springer
ISBN 13 : 3319309218
Total Pages : 308 pages
Book Rating : 4.17/5 ( download)

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Download or read book Numerical Optimization with Computational Errors written by Alexander J. Zaslavski and published by Springer. This book was released on 2016-04-22 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book studies the approximate solutions of optimization problems in the presence of computational errors. A number of results are presented on the convergence behavior of algorithms in a Hilbert space; these algorithms are examined taking into account computational errors. The author illustrates that algorithms generate a good approximate solution, if computational errors are bounded from above by a small positive constant. Known computational errors are examined with the aim of determining an approximate solution. Researchers and students interested in the optimization theory and its applications will find this book instructive and informative. This monograph contains 16 chapters; including a chapters devoted to the subgradient projection algorithm, the mirror descent algorithm, gradient projection algorithm, the Weiszfelds method, constrained convex minimization problems, the convergence of a proximal point method in a Hilbert space, the continuous subgradient method, penalty methods and Newton’s method.

Author : Michael C. Ferris
Publisher : SIAM
ISBN 13 : 9780898713916
Total Pages : 494 pages
Book Rating : 4.19/5 ( download)

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Download or read book Complementarity and Variational Problems written by Michael C. Ferris and published by SIAM. This book was released on 1997-01-01 with total page 494 pages. Available in PDF, EPUB and Kindle. Book excerpt: After more than three decades of research, the subject of complementarity problems and its numerous extensions has become a well-established and fruitful discipline within mathematical programming and applied mathematics. Sources of these problems are diverse and span numerous areas in engineering, economics, and the sciences. Includes refereed articles.

Author : A. F. Izmailov
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.99/5 ( download)

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Download or read book On Error Bounds Ans Newton-type Methods for Generalized Nash Equilibriium Problems written by A. F. Izmailov and published by . This book was released on 2012 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Error bounds (estimates for the distance to the solution set of a given problem) are key to analyzing convergence rates, or often even to justifying convergence itself, of computational methods for solving the problem in question. That said, for the generalized Nash equilibrium problems (GNEP), the theory of error bounds had not been developed in depth comparable to the fields of optimization and variational problems. In this paper, we provide a systematic approach which should be useful for verifying error bounds for both specifc instances of GNEPs and for classes of GNEPs. These results on error bounds cover those (few) that existed previously but go beyond. In addition, they readily imply a Lipschitzian stability result for solutions of GNEPs, a subject where again very little had been known. As a specific application of error bounds, we discuss Newtonian methods for solving GNEPs. While we do not propose any significantly new methods in this respect, some new insights into applicability to GNEPs of various approaches and into their convergence properties are presented.

Author : C. T. Kelley
Publisher : SIAM
ISBN 13 : 9781611970920
Total Pages : 195 pages
Book Rating : 4.2X/5 ( download)

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Download or read book Iterative Methods for Optimization written by C. T. Kelley and published by SIAM. This book was released on 1999-01-01 with total page 195 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a carefully selected group of methods for unconstrained and bound constrained optimization problems and analyzes them in depth both theoretically and algorithmically. It focuses on clarity in algorithmic description and analysis rather than generality, and while it provides pointers to the literature for the most general theoretical results and robust software, the author thinks it is more important that readers have a complete understanding of special cases that convey essential ideas. A companion to Kelley's book, Iterative Methods for Linear and Nonlinear Equations (SIAM, 1995), this book contains many exercises and examples and can be used as a text, a tutorial for self-study, or a reference. Iterative Methods for Optimization does more than cover traditional gradient-based optimization: it is the first book to treat sampling methods, including the Hooke-Jeeves, implicit filtering, MDS, and Nelder-Mead schemes in a unified way, and also the first book to make connections between sampling methods and the traditional gradient-methods. Each of the main algorithms in the text is described in pseudocode, and a collection of MATLAB codes is available. Thus, readers can experiment with the algorithms in an easy way as well as implement them in other languages.

Author : Asen L. Dontchev
Publisher : Springer Nature
ISBN 13 : 3030799115
Total Pages : 223 pages
Book Rating : 4.13/5 ( download)

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Download or read book Lectures on Variational Analysis written by Asen L. Dontchev and published by Springer Nature. This book was released on 2022-02-04 with total page 223 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Francisco Facchinei
Publisher : Springer Science & Business Media
ISBN 13 : 0387218157
Total Pages : 698 pages
Book Rating : 4.51/5 ( download)

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Download or read book Finite-Dimensional Variational Inequalities and Complementarity Problems written by Francisco Facchinei and published by Springer Science & Business Media. This book was released on 2007-06-04 with total page 698 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is part two of a two-volume work presenting a comprehensive treatment of the finite-dimensional variational inequality and complementarity problem. It details algorithms for solving finite dimensional variational inequalities and complementarity problems. Coverage includes abundant exercises as well as an extensive bibliography. The book will be an enduring reference on the subject and provide the foundation for its sustained growth.