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.
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.
Download or read book Stabilized Sequential Quadratic Programming for Optimization and a Stabilized Newton type Method for Variational Problems written by Damián Fernández and published by . This book was released on 2007 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Stabilized Sequential Quadratic Programming for Optimization and a Stabilized Newton type Method for Variational Problems Without Constraint Qualifications written by Damián Fernández and published by . This book was released on 2007 with total page 23 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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.
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:
Download or read book Convex Analysis and Variational Problems written by Ivar Ekeland and published by SIAM. This book was released on 1999-12-01 with total page 414 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains different developments of infinite dimensional convex programming in the context of convex analysis, including duality, minmax and Lagrangians, and convexification of nonconvex optimization problems in the calculus of variations (infinite dimension). It also includes the theory of convex duality applied to partial differential equations; no other reference presents this in a systematic way. The minmax theorems contained in this book have many useful applications, in particular the robust control of partial differential equations in finite time horizon. First published in English in 1976, this SIAM Classics in Applied Mathematics edition contains the original text along with a new preface and some additional references.
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.
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.
Download or read book Lagrange Multiplier Approach to Variational Problems and Applications written by Kazufumi Ito and published by SIAM. This book was released on 2008-11-06 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: Analyses Lagrange multiplier theory and demonstrates its impact on the development of numerical algorithms for variational problems in function spaces.
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.
Download or read book Nonlinear Analysis and Variational Problems written by Panos M. Pardalos and published by Springer Science & Business Media. This book was released on 2009-10-20 with total page 502 pages. Available in PDF, EPUB and Kindle. Book excerpt: The chapters in this volume, written by international experts from different fields of mathematics, are devoted to honoring George Isac, a renowned mathematician. These contributions focus on recent developments in complementarity theory, variational principles, stability theory of functional equations, nonsmooth optimization, and several other important topics at the forefront of nonlinear analysis and optimization.
Download or read book Variational Analysis and Applications written by Boris S. Mordukhovich and published by Springer. This book was released on 2018-08-02 with total page 636 pages. Available in PDF, EPUB and Kindle. Book excerpt: Building on fundamental results in variational analysis, this monograph presents new and recent developments in the field as well as selected applications. Accessible to a broad spectrum of potential readers, the main material is presented in finite-dimensional spaces. Infinite-dimensional developments are discussed at the end of each chapter with comprehensive commentaries which emphasize the essence of major results, track the genesis of ideas, provide historical comments, and illuminate challenging open questions and directions for future research. The first half of the book (Chapters 1–6) gives a systematic exposition of key concepts and facts, containing basic material as well as some recent and new developments. These first chapters are particularly accessible to masters/doctoral students taking courses in modern optimization, variational analysis, applied analysis, variational inequalities, and variational methods. The reader’s development of skills will be facilitated as they work through each, or a portion of, the multitude of exercises of varying levels. Additionally, the reader may find hints and references to more difficult exercises and are encouraged to receive further inspiration from the gems in chapter commentaries. Chapters 7–10 focus on recent results and applications of variational analysis to advanced problems in modern optimization theory, including its hierarchical and multiobjective aspects, as well as microeconomics, and related areas. It will be of great use to researchers and professionals in applied and behavioral sciences and engineering.
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.
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.
Download or read book Progress in Optimization written by Andrew Eberhard and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 309 pages. Available in PDF, EPUB and Kindle. Book excerpt: Although the monograph Progress in Optimization I: Contributions from Aus tralasia grew from the idea of publishing a proceedings of the Fourth Optimiza tion Day, held in July 1997 at the Royal Melbourne Institute of Technology, the focus soon changed to a refereed volume in optimization. The intention is to publish a similar book annually, following each Optimization Day. The idea of having an annual Optimization Day was conceived by Barney Glover; the first of these Optimization Days was held in 1994 at the University of Ballarat. Barney hoped that such a yearly event would bring together the many, but widely dispersed, researchers in Australia who were publishing in optimization and related areas such as control. The first Optimization Day event was followed by similar conferences at The University of New South Wales (1995), The University of Melbourne (1996), the Royal Melbourne Institute of Technology (1997), and The University of Western Australia (1998). The 1999 conference will return to Ballarat University, being organized by Barney's long-time collaborator Alex Rubinov. In recent years the Optimization Day has been held in conjunction with other locally-held national or international conferences. This has widened the scope of the monograph with contributions not only coming from researchers in Australia and neighboring regions but also from their collaborators in Europe and North America.
Download or read book Computational Optimization written by Jong-Shi Pang and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computational Optimization: A Tribute to Olvi Mangasarian serves as an excellent reference, providing insight into some of the most challenging research issues in the field. This collection of papers covers a wide spectrum of computational optimization topics, representing a blend of familiar nonlinear programming topics and such novel paradigms as semidefinite programming and complementarity-constrained nonlinear programs. Many new results are presented in these papers which are bound to inspire further research and generate new avenues for applications. An informal categorization of the papers includes: Algorithmic advances for special classes of constrained optimization problems Analysis of linear and nonlinear programs Algorithmic advances B- stationary points of mathematical programs with equilibrium constraints Applications of optimization Some mathematical topics Systems of nonlinear equations.
