The Pitfalls Of Convergence Analysis

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Weak Convergence Methods and Singularly Perturbed Stochastic Control and Filtering Problems

Author : Harold Kushner
Publisher : Springer Science & Business Media
ISBN 13 : 146124482X
Total Pages : 245 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Weak Convergence Methods and Singularly Perturbed Stochastic Control and Filtering Problems by : Harold Kushner

Download or read book Weak Convergence Methods and Singularly Perturbed Stochastic Control and Filtering Problems written by Harold Kushner and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 245 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book deals with several closely related topics concerning approxima tions and perturbations of random processes and their applications to some important and fascinating classes of problems in the analysis and design of stochastic control systems and nonlinear filters. The basic mathematical methods which are used and developed are those of the theory of weak con vergence. The techniques are quite powerful for getting weak convergence or functional limit theorems for broad classes of problems and many of the techniques are new. The original need for some of the techniques which are developed here arose in connection with our study of the particular applica tions in this book, and related problems of approximation in control theory, but it will be clear that they have numerous applications elsewhere in weak convergence and process approximation theory. The book is a continuation of the author's long term interest in problems of the approximation of stochastic processes and its applications to problems arising in control and communication theory and related areas. In fact, the techniques used here can be fruitfully applied to many other areas. The basic random processes of interest can be described by solutions to either (multiple time scale) Ito differential equations driven by wide band or state dependent wide band noise or which are singularly perturbed. They might be controlled or not, and their state values might be fully observable or not (e. g. , as in the nonlinear filtering problem).

Mathematical Analysis of Deterministic and Stochastic Problems in Complex Media Electromagnetics

Author : G. F. Roach
Publisher : Princeton University Press
ISBN 13 : 1400842654
Total Pages : 400 pages
Book Rating : 4.4/5 (8 download)

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Book Synopsis Mathematical Analysis of Deterministic and Stochastic Problems in Complex Media Electromagnetics by : G. F. Roach

Download or read book Mathematical Analysis of Deterministic and Stochastic Problems in Complex Media Electromagnetics written by G. F. Roach and published by Princeton University Press. This book was released on 2012-03-04 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: Electromagnetic complex media are artificial materials that affect the propagation of electromagnetic waves in surprising ways not usually seen in nature. Because of their wide range of important applications, these materials have been intensely studied over the past twenty-five years, mainly from the perspectives of physics and engineering. But a body of rigorous mathematical theory has also gradually developed, and this is the first book to present that theory. Designed for researchers and advanced graduate students in applied mathematics, electrical engineering, and physics, this book introduces the electromagnetics of complex media through a systematic, state-of-the-art account of their mathematical theory. The book combines the study of well posedness, homogenization, and controllability of Maxwell equations complemented with constitutive relations describing complex media. The book treats deterministic and stochastic problems both in the frequency and time domains. It also covers computational aspects and scattering problems, among other important topics. Detailed appendices make the book self-contained in terms of mathematical prerequisites, and accessible to engineers and physicists as well as mathematicians.

Ill-Posed and Inverse Problems

Author : Vladimir G. Romanov
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110942011
Total Pages : 484 pages
Book Rating : 4.1/5 (19 download)

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Book Synopsis Ill-Posed and Inverse Problems by : Vladimir G. Romanov

Download or read book Ill-Posed and Inverse Problems written by Vladimir G. Romanov and published by Walter de Gruyter GmbH & Co KG. This book was released on 2018-11-05 with total page 484 pages. Available in PDF, EPUB and Kindle. Book excerpt: M.M. Lavrentiev is the author of many fundamental scientific results in many directions of mathematics and its applications, such as differential equations, inverse and ill-posed problems, tomography, numerical and applied mathematics. His results in the theory of inverse problems for differential equations and in tomography are well known all over the world. To honour him on the occasion of his 70th birthday renowned scientists in this field of mathematics, both from East and West, have contributed to this special collection of papers on ill-posed and inverse problems, which will be of interest to anyone working in this field.

Economic Growth and Convergence

Author : Michał Bernardelli
Publisher : Routledge
ISBN 13 : 1000407233
Total Pages : 164 pages
Book Rating : 4.0/5 (4 download)

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Book Synopsis Economic Growth and Convergence by : Michał Bernardelli

Download or read book Economic Growth and Convergence written by Michał Bernardelli and published by Routledge. This book was released on 2021-06-30 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt: There are many different types of convergence within economics, as well as several methods to analyse each of them. This book addresses the concept of real economic convergence or the gradual levelling-off of GDP (gross domestic product) per capita rates across economies. In addition to a detailed, holistic overview of the history and theory, the authors include a description of two modern methods of assessing the occurrence and rate of convergence, BMA-based and HMM-based, as well as the results of the empirical analysis. Readers will have access not only to the conventional econometric approach of β convergence but also to an alternative one, allowing for the convergence issue to be expressed in the context of automatic pattern recognition. This approach is universal as it can be adapted to a variety of input data. The lowest aggregation level study investigates regional convergence through the case of Polish voivodships, where convergence towards the leader is tested. On a higher level of aggregation, the authors examine the existence of GDP convergence in such groups as the EU28, North Africa and the Middle East, sub-Saharan Africa, South America, Caribbean, South-East Asia, Australia and Oceania, or post-socialist countries. For each group, the real β convergence is tested using the two above-mentioned approaches. The results are widely discussed, broadly illustrated, interpreted, and compared. The analysis allows readers to draw interesting conclusions about the causes of convergence or the drivers behind divergence. The book will stimulate further research in the field, but the research was conducted from the point of view of individual countries.

Approximate Global Convergence and Adaptivity for Coefficient Inverse Problems

Author : Larisa Beilina
Publisher : Springer Science & Business Media
ISBN 13 : 1441978054
Total Pages : 420 pages
Book Rating : 4.4/5 (419 download)

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Book Synopsis Approximate Global Convergence and Adaptivity for Coefficient Inverse Problems by : Larisa Beilina

Download or read book Approximate Global Convergence and Adaptivity for Coefficient Inverse Problems written by Larisa Beilina and published by Springer Science & Business Media. This book was released on 2012-03-09 with total page 420 pages. Available in PDF, EPUB and Kindle. Book excerpt: Approximate Global Convergence and Adaptivity for Coefficient Inverse Problems is the first book in which two new concepts of numerical solutions of multidimensional Coefficient Inverse Problems (CIPs) for a hyperbolic Partial Differential Equation (PDE) are presented: Approximate Global Convergence and the Adaptive Finite Element Method (adaptivity for brevity). Two central questions for CIPs are addressed: How to obtain a good approximations for the exact solution without any knowledge of a small neighborhood of this solution, and how to refine it given the approximation. The book also combines analytical convergence results with recipes for various numerical implementations of developed algorithms. The developed technique is applied to two types of blind experimental data, which are collected both in a laboratory and in the field. The result for the blind backscattering experimental data collected in the field addresses a real world problem of imaging of shallow explosives.

The Master Equation and the Convergence Problem in Mean Field Games

Author : Pierre Cardaliaguet
Publisher : Princeton University Press
ISBN 13 : 0691190712
Total Pages : 224 pages
Book Rating : 4.6/5 (911 download)

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Book Synopsis The Master Equation and the Convergence Problem in Mean Field Games by : Pierre Cardaliaguet

Download or read book The Master Equation and the Convergence Problem in Mean Field Games written by Pierre Cardaliaguet and published by Princeton University Press. This book was released on 2019-08-13 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes the latest advances in the theory of mean field games, which are optimal control problems with a continuum of players, each of them interacting with the whole statistical distribution of a population. While it originated in economics, this theory now has applications in areas as diverse as mathematical finance, crowd phenomena, epidemiology, and cybersecurity. Because mean field games concern the interactions of infinitely many players in an optimal control framework, one expects them to appear as the limit for Nash equilibria of differential games with finitely many players as the number of players tends to infinity. This book rigorously establishes this convergence, which has been an open problem until now. The limit of the system associated with differential games with finitely many players is described by the so-called master equation, a nonlocal transport equation in the space of measures. After defining a suitable notion of differentiability in the space of measures, the authors provide a complete self-contained analysis of the master equation. Their analysis includes the case of common noise problems in which all the players are affected by a common Brownian motion. They then go on to explain how to use the master equation to prove the mean field limit. This groundbreaking book presents two important new results in mean field games that contribute to a unified theoretical framework for this exciting and fast-developing area of mathematics.

Convergence Analysis of Proximal-like Methods for Variational Inequalities and Fixed Point Problems

Author : Nils Langenberg
Publisher : Logos Verlag Berlin GmbH
ISBN 13 : 3832528903
Total Pages : 255 pages
Book Rating : 4.8/5 (325 download)

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Book Synopsis Convergence Analysis of Proximal-like Methods for Variational Inequalities and Fixed Point Problems by : Nils Langenberg

Download or read book Convergence Analysis of Proximal-like Methods for Variational Inequalities and Fixed Point Problems written by Nils Langenberg and published by Logos Verlag Berlin GmbH. This book was released on 2011 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt: Several regularization methods for variational inequalities and fixed point problems are studied. Known convergence results especially require some kind of monotonicity of the problem data as well as, especially for Bregman-function-based algorithms, some additional assumption known as the cutting plane property. Unfortunately, these assumptions may be considered as rather restrictive e.g. in the framework of Nash equilibrium problems. This motivates the development of convergence results under weaker hypotheses which constitute the major subject of the present book. Studied methods include the Bregman-function-based Proximal Point Algorithm (BPPA), Cohen's Auxiliary Problem Principle and an extragradient algorithm.Moreover, this work also contains the first numerical comparison of stopping criteria in the framework of the BPPA. Although such conditions are the subject of theoretical investigations frequently, their numerical effectiveness and a deducible preference were still unknown. This gives rise to the necessity of the presented numerical experiments.

Computational Intelligence in Expensive Optimization Problems

Author : Yoel Tenne
Publisher : Springer Science & Business Media
ISBN 13 : 364210701X
Total Pages : 736 pages
Book Rating : 4.6/5 (421 download)

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Book Synopsis Computational Intelligence in Expensive Optimization Problems by : Yoel Tenne

Download or read book Computational Intelligence in Expensive Optimization Problems written by Yoel Tenne and published by Springer Science & Business Media. This book was released on 2010-03-10 with total page 736 pages. Available in PDF, EPUB and Kindle. Book excerpt: In modern science and engineering, laboratory experiments are replaced by high fidelity and computationally expensive simulations. Using such simulations reduces costs and shortens development times but introduces new challenges to design optimization process. Examples of such challenges include limited computational resource for simulation runs, complicated response surface of the simulation inputs-outputs, and etc. Under such difficulties, classical optimization and analysis methods may perform poorly. This motivates the application of computational intelligence methods such as evolutionary algorithms, neural networks and fuzzy logic, which often perform well in such settings. This is the first book to introduce the emerging field of computational intelligence in expensive optimization problems. Topics covered include: dedicated implementations of evolutionary algorithms, neural networks and fuzzy logic. reduction of expensive evaluations (modelling, variable-fidelity, fitness inheritance), frameworks for optimization (model management, complexity control, model selection), parallelization of algorithms (implementation issues on clusters, grids, parallel machines), incorporation of expert systems and human-system interface, single and multiobjective algorithms, data mining and statistical analysis, analysis of real-world cases (such as multidisciplinary design optimization). The edited book provides both theoretical treatments and real-world insights gained by experience, all contributed by leading researchers in the respective fields. As such, it is a comprehensive reference for researchers, practitioners, and advanced-level students interested in both the theory and practice of using computational intelligence for expensive optimization problems.

Solutions of Fixed Point Problems with Computational Errors

Author : Alexander J. Zaslavski
Publisher : Springer Nature
ISBN 13 : 3031508793
Total Pages : 392 pages
Book Rating : 4.0/5 (315 download)

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Book Synopsis Solutions of Fixed Point Problems with Computational Errors by : Alexander J. Zaslavski

Download or read book Solutions of Fixed Point Problems with Computational Errors written by Alexander J. Zaslavski and published by Springer Nature. This book was released on with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Efficient Online Learning Algorithms for Total Least Square Problems

Author : Xiangyu Kong
Publisher : Springer Nature
ISBN 13 : 9819717655
Total Pages : 288 pages
Book Rating : 4.8/5 (197 download)

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Book Synopsis Efficient Online Learning Algorithms for Total Least Square Problems by : Xiangyu Kong

Download or read book Efficient Online Learning Algorithms for Total Least Square Problems written by Xiangyu Kong and published by Springer Nature. This book was released on with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Newton-Type Methods for Optimization and Variational Problems

Author : Alexey F. Izmailov
Publisher : Springer
ISBN 13 : 3319042475
Total Pages : 587 pages
Book Rating : 4.3/5 (19 download)

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Book Synopsis Newton-Type Methods for Optimization and Variational Problems by : Alexey F. Izmailov

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.

Numerical Methods for Optimal Control Problems with State Constraints

Author : Radoslaw Pytlak
Publisher : Springer
ISBN 13 : 3540486623
Total Pages : 224 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Numerical Methods for Optimal Control Problems with State Constraints by : Radoslaw Pytlak

Download or read book Numerical Methods for Optimal Control Problems with State Constraints written by Radoslaw Pytlak and published by Springer. This book was released on 2006-11-14 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: While optimality conditions for optimal control problems with state constraints have been extensively investigated in the literature the results pertaining to numerical methods are relatively scarce. This book fills the gap by providing a family of new methods. Among others, a novel convergence analysis of optimal control algorithms is introduced. The analysis refers to the topology of relaxed controls only to a limited degree and makes little use of Lagrange multipliers corresponding to state constraints. This approach enables the author to provide global convergence analysis of first order and superlinearly convergent second order methods. Further, the implementation aspects of the methods developed in the book are presented and discussed. The results concerning ordinary differential equations are then extended to control problems described by differential-algebraic equations in a comprehensive way for the first time in the literature.

The Mimetic Finite Difference Method for Elliptic Problems

Author : Lourenco Beirao da Veiga
Publisher : Springer
ISBN 13 : 3319026631
Total Pages : 399 pages
Book Rating : 4.3/5 (19 download)

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Book Synopsis The Mimetic Finite Difference Method for Elliptic Problems by : Lourenco Beirao da Veiga

Download or read book The Mimetic Finite Difference Method for Elliptic Problems written by Lourenco Beirao da Veiga and published by Springer. This book was released on 2014-05-22 with total page 399 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes the theoretical and computational aspects of the mimetic finite difference method for a wide class of multidimensional elliptic problems, which includes diffusion, advection-diffusion, Stokes, elasticity, magnetostatics and plate bending problems. The modern mimetic discretization technology developed in part by the Authors allows one to solve these equations on unstructured polygonal, polyhedral and generalized polyhedral meshes. The book provides a practical guide for those scientists and engineers that are interested in the computational properties of the mimetic finite difference method such as the accuracy, stability, robustness, and efficiency. Many examples are provided to help the reader to understand and implement this method. This monograph also provides the essential background material and describes basic mathematical tools required to develop further the mimetic discretization technology and to extend it to various applications.

Advanced Data Mining and Applications

Author : Xiaochun Yang
Publisher : Springer Nature
ISBN 13 : 3031466640
Total Pages : 722 pages
Book Rating : 4.0/5 (314 download)

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Book Synopsis Advanced Data Mining and Applications by : Xiaochun Yang

Download or read book Advanced Data Mining and Applications written by Xiaochun Yang and published by Springer Nature. This book was released on 2023-12-06 with total page 722 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 19th International Conference on Advanced Data Mining and Applications, ADMA 2023, held in Shenyang, China, during August 21–23, 2023. The 216 full papers included in this book were carefully reviewed and selected from 503 submissions. They were organized in topical sections as follows: Data mining foundations, Grand challenges of data mining, Parallel and distributed data mining algorithms, Mining on data streams, Graph mining and Spatial data mining.

Nonlinear Programming and Variational Inequality Problems

Author : Michael Patriksson
Publisher : Springer Science & Business Media
ISBN 13 : 147572991X
Total Pages : 343 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis Nonlinear Programming and Variational Inequality Problems by : Michael Patriksson

Download or read book Nonlinear Programming and Variational Inequality Problems written by Michael Patriksson and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 343 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since I started working in the area of nonlinear programming and, later on, variational inequality problems, I have frequently been surprised to find that many algorithms, however scattered in numerous journals, monographs and books, and described rather differently, are closely related to each other. This book is meant to help the reader understand and relate algorithms to each other in some intuitive fashion, and represents, in this respect, a consolidation of the field. The framework of algorithms presented in this book is called Cost Approxi mation. (The preface of the Ph.D. thesis [Pat93d] explains the background to the work that lead to the thesis, and ultimately to this book.) It describes, for a given formulation of a variational inequality or nonlinear programming problem, an algorithm by means of approximating mappings and problems, a principle for the update of the iteration points, and a merit function which guides and monitors the convergence of the algorithm. One purpose of this book is to offer this framework as an intuitively appeal ing tool for describing an algorithm. One of the advantages of the framework, or any reasonable framework for that matter, is that two algorithms may be easily related and compared through its use. This framework is particular in that it covers a vast number of methods, while still being fairly detailed; the level of abstraction is in fact the same as that of the original problem statement.

Variational Inequalities and Network Equilibrium Problems

Author : F. Giannessi
Publisher : Springer Science & Business Media
ISBN 13 : 1489913580
Total Pages : 304 pages
Book Rating : 4.4/5 (899 download)

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Book Synopsis Variational Inequalities and Network Equilibrium Problems by : F. Giannessi

Download or read book Variational Inequalities and Network Equilibrium Problems written by F. Giannessi and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume brings forth a set of papers presented at the conference on "Varia tional Inequalities and network equilibrium problems", held in Erice at the "G. Stam pacchia" School of the "E. Majorana" Centre for Scientific Culture in the period 19~25 June 1994. The meeting was conceived to contribute to the exchange between Variational Analysis and equilibrium problems, especially those related to network design. Most of the approaches and viewpoints of these fields are present in the volume, both as concerns the theory and the applications of equilibrium problems to transportation, computer and electric networks, to market behavior, and to bi~level programming. Being convinced of the great importance of equilibrium problems as well as of their complexity, the organizers hope that the merging of points of view coming from differ ent fields will stimulate theoretical research and applications. In this context Variational and Quasi~Variational Inequalities have shown them selves to be very important models for equilibrium problems. As a consequence in the last two decades they have received a lot of attention both as to mathematical inves tigation and applications. The proof that the above mentioned equilibrium problems can be expressed, in terms of Variational or Quasi~Variational Inequalities also in the non~standard and non~symmetric cases, has been a crucial improvement.

Optimization on Solution Sets of Common Fixed Point Problems

Author : Alexander J. Zaslavski
Publisher : Springer Nature
ISBN 13 : 3030788490
Total Pages : 434 pages
Book Rating : 4.0/5 (37 download)

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Book Synopsis Optimization on Solution Sets of Common Fixed Point Problems by : Alexander J. Zaslavski

Download or read book Optimization on Solution Sets of Common Fixed Point Problems written by Alexander J. Zaslavski and published by Springer Nature. This book was released on 2021-08-09 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to a detailed study of the subgradient projection method and its variants for convex optimization problems over the solution sets of common fixed point problems and convex feasibility problems. These optimization problems are investigated to determine good solutions obtained by different versions of the subgradient projection algorithm in the presence of sufficiently small computational errors. The use of selected algorithms is highlighted including the Cimmino type subgradient, the iterative subgradient, and the dynamic string-averaging subgradient. All results presented are new. Optimization problems where the underlying constraints are the solution sets of other problems, frequently occur in applied mathematics. The reader should not miss the section in Chapter 1 which considers some examples arising in the real world applications. The problems discussed have an important impact in optimization theory as well. The book will be useful for researches interested in the optimization theory and its applications.