Special Issue On Set Convergence In Nonlinear Analysis And Optimization

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Recent Developments in Well-Posed Variational Problems

Author : Roberto Lucchetti
Publisher : Springer Science & Business Media
ISBN 13 : 9401584729
Total Pages : 271 pages
Book Rating : 4.4/5 (15 download)

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Book Synopsis Recent Developments in Well-Posed Variational Problems by : Roberto Lucchetti

Download or read book Recent Developments in Well-Posed Variational Problems written by Roberto Lucchetti and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 271 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains several surveys focused on the ideas of approximate solutions, well-posedness and stability of problems in scalar and vector optimization, game theory and calculus of variations. These concepts are of particular interest in many fields of mathematics. The idea of stability goes back at least to J. Hadamard who introduced it in the setting of differential equations; the concept of well-posedness for minimum problems is more recent (the mid-sixties) and originates with A.N. Tykhonov. It turns out that there are connections between the two properties in the sense that a well-posed problem which, at least in principle, is "easy to solve", has a solution set that does not vary too much under perturbation of the data of the problem, i.e. it is "stable". These themes have been studied in depth for minimum problems and now we have a general picture of the related phenomena in this case. But, of course, the same concepts can be studied in other more complicated situations as, e.g. vector optimization, game theory and variational inequalities. Let us mention that in several of these new areas there is not even a unique idea of what should be called approximate solution, and the latter is at the basis of the definition of well posed problem.

Nonlinear Analysis and Optimization I

Author : Simeon Reich
Publisher : American Mathematical Soc.
ISBN 13 : 0821848348
Total Pages : 290 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Nonlinear Analysis and Optimization I by : Simeon Reich

Download or read book Nonlinear Analysis and Optimization I written by Simeon Reich and published by American Mathematical Soc.. This book was released on 2010 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is the first of two volumes representing leading themes of current research in nonlinear analysis and optimization. The articles are written by prominent researchers in these two areas and bring the readers, advanced graduate students and researchers alike, to the frontline of the vigorous research in these important fields of mathematics. This volume contains articles on nonlinear analysis. Topics covered include the convex feasibility problem, fixed point theory, mathematical biology, Mosco stability, nonexpansive mapping theory, nonlinear partial differential equations, optimal control, the proximal point algorithm and semigroup theory. The companion volume (Contemporary Mathematics, Volume 514) is devoted to optimization. This book is co-published with Bar-Ilan University (Ramat-Gan, Israel). Table of Contents: A. S. Ackleh, K. Deng, and Q. Huang -- Existence-uniqueness results and difference approximations for an amphibian juvenile-adult model; S. Aizicovici, N. S. Papageorgiou, and V. Staicu -- Three nontrivial solutions for $p$-Laplacian Neumann problems with a concave nonlinearity near the origin; V. Barbu -- Optimal stabilizable feedback controller for Navier-Stokes equations; H. H. Bauschke and X. Wang -- Firmly nonexpansive and Kirszbraun-Valentine extensions: A constructive approach via monotone operator theory; R. E. Bruck -- On the random product of orthogonal projections in Hilbert space II; D. Butnariu, E. Resmerita, and S. Sabach -- A Mosco stability theorem for the generalized proximal mapping; A. Cegielski -- Generalized relaxations of nonexpansive operators and convex feasibility problems; Y. Censor and A. Segal -- Sparse string-averaging and split common fixed points; T. Dominguez Benavides and S. Phothi -- Genericity of the fixed point property for reflexive spaces under renormings; K. Goebel and B. Sims -- Mean Lipschitzian mappings; T. Ibaraki and W. Takahashi -- Generalized nonexpansive mappings and a proximal-type algorithm in Banach spaces; W. Kaczor, T. Kuczumow, and N. Michalska -- The common fixed point set of commuting nonexpansive mapping in Cartesian products of weakly compact convex sets; L. Leu'tean -- Nonexpansive iterations in uniformly convex $W$-hyperbolic spaces; G. Lopez, V. Martin-Marquez, and H.-K. Xu -- Halpern's iteration for nonexpansive mappings; J. W. Neuberger -- Lie generators for local semigroups; H.-K. Xu -- An alternative regularization method for nonexpansive mappings with applications. (CONM/513)

Nonlinear Analysis

Author : Leszek Gasinski
Publisher : CRC Press
ISBN 13 : 9781584884842
Total Pages : 992 pages
Book Rating : 4.8/5 (848 download)

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Book Synopsis Nonlinear Analysis by : Leszek Gasinski

Download or read book Nonlinear Analysis written by Leszek Gasinski and published by CRC Press. This book was released on 2005-07-27 with total page 992 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear analysis is a broad, interdisciplinary field characterized by a remarkable mixture of analysis, topology, and applications. Its concepts and techniques provide the tools for developing more realistic and accurate models for a variety of phenomena encountered in fields ranging from engineering and chemistry to economics and biology. This volume focuses on topics in nonlinear analysis pertinent to the theory of boundary value problems and their application in areas such as control theory and the calculus of variations. It complements the many other books on nonlinear analysis by addressing topics previously discussed fully only in scattered research papers. These include recent results on critical point theory, nonlinear differential operators, and related regularity and comparison principles. The rich variety of topics, both theoretical and applied, make Nonlinear Analysis useful to anyone, whether graduate student or researcher, working in analysis or its applications in optimal control, theoretical mechanics, or dynamical systems. An appendix contains all of the background material needed, and a detailed bibliography forms a guide for further study.

NBS Special Publication

Author :
Publisher :
ISBN 13 :
Total Pages : 416 pages
Book Rating : 4.F/5 ( download)

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Book Synopsis NBS Special Publication by :

Download or read book NBS Special Publication written by and published by . This book was released on 1968 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Nonlinear Analysis and Optimization

Author : Boris S. Mordukhovich
Publisher : American Mathematical Soc.
ISBN 13 : 1470417367
Total Pages : 330 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Nonlinear Analysis and Optimization by : Boris S. Mordukhovich

Download or read book Nonlinear Analysis and Optimization written by Boris S. Mordukhovich and published by American Mathematical Soc.. This book was released on 2016-02-26 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the IMU/AMS Special Session on Nonlinear Analysis and Optimization, held from June 16-19, 2014, at the Second Joint International Meeting of the Israel Mathematical Union (IMU) and the American Mathematical Society (AMS), Bar-Ilan and Tel-Aviv Universities, Israel, and the Workshop on Nonlinear Analysis and Optimization, held on June 12, 2014, at the Technion-Israel Institute of Technology. The papers in this volume cover many different topics in Nonlinear Analysis and Optimization, including: Taylor domination property for analytic functions in the complex disk, mappings with upper integral bounds for p -moduli, multiple Fourier transforms and trigonometric series in line with Hardy's variation, finite-parameter feedback control for stabilizing damped nonlinear wave equations, implicit Euler approximation and optimization of one-sided Lipschitz differential inclusions, Bolza variational problems with extended-valued integrands on large intervals, first order singular variational problem with nonconvex cost, gradient and extragradient methods for the elasticity imaging inverse problem, discrete approximations of the entropy functional for probability measures on the plane, optimal irrigation scheduling for wheat production, existence of a fixed point of nonexpansive mappings in uniformly convex Banach spaces, strong convergence properties of m-accretive bounded operators, the Reich-Simons convex analytic inequality, nonlinear input-output equilibrium, differential linear-quadratic Nash games with mixed state-control constraints, and excessive revenue models of competitive markets.

Variational Convergence And Stochastic Homogenization Of Nonlinear Reaction-diffusion Problems

Author : Omar Anza Hafsa
Publisher : World Scientific
ISBN 13 : 9811258503
Total Pages : 321 pages
Book Rating : 4.8/5 (112 download)

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Book Synopsis Variational Convergence And Stochastic Homogenization Of Nonlinear Reaction-diffusion Problems by : Omar Anza Hafsa

Download or read book Variational Convergence And Stochastic Homogenization Of Nonlinear Reaction-diffusion Problems written by Omar Anza Hafsa and published by World Scientific. This book was released on 2022-06-21 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: A substantial number of problems in physics, chemical physics, and biology, are modeled through reaction-diffusion equations to describe temperature distribution or chemical substance concentration. For problems arising from ecology, sociology, or population dynamics, they describe the density of some populations or species. In this book the state variable is a concentration, or a density according to the cases. The reaction function may be complex and include time delays terms that model various situations involving maturation periods, resource regeneration times, or incubation periods. The dynamics may occur in heterogeneous media and may depend upon a small or large parameter, as well as the reaction term. From a purely formal perspective, these parameters are indexed by n. Therefore, reaction-diffusion equations give rise to sequences of Cauchy problems.The first part of the book is devoted to the convergence of these sequences in a sense made precise in the book. The second part is dedicated to the specific case when the reaction-diffusion problems depend on a small parameter ∊ₙ intended to tend towards 0. This parameter accounts for the size of small spatial and randomly distributed heterogeneities. The convergence results obtained in the first part, with additionally some probabilistic tools, are applied to this specific situation. The limit problems are illustrated through biological invasion, food-limited or prey-predator models where the interplay between environment heterogeneities in the individual evolution of propagation species plays an essential role. They provide a description in terms of deterministic and homogeneous reaction-diffusion equations, for which numerical schemes are possible.

Nonlinear Analysis - Theory and Methods

Author : Nikolaos S. Papageorgiou
Publisher : Springer
ISBN 13 : 3030034305
Total Pages : 586 pages
Book Rating : 4.0/5 (3 download)

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Book Synopsis Nonlinear Analysis - Theory and Methods by : Nikolaos S. Papageorgiou

Download or read book Nonlinear Analysis - Theory and Methods written by Nikolaos S. Papageorgiou and published by Springer. This book was released on 2019-02-26 with total page 586 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book emphasizes those basic abstract methods and theories that are useful in the study of nonlinear boundary value problems. The content is developed over six chapters, providing a thorough introduction to the techniques used in the variational and topological analysis of nonlinear boundary value problems described by stationary differential operators. The authors give a systematic treatment of the basic mathematical theory and constructive methods for these classes of nonlinear equations as well as their applications to various processes arising in the applied sciences. They show how these diverse topics are connected to other important parts of mathematics, including topology, functional analysis, mathematical physics, and potential theory. Throughout the book a nice balance is maintained between rigorous mathematics and physical applications. The primary readership includes graduate students and researchers in pure and applied nonlinear analysis.

Mathematical Reviews

Author :
Publisher :
ISBN 13 :
Total Pages : 1432 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Mathematical Reviews by :

Download or read book Mathematical Reviews written by and published by . This book was released on 2003 with total page 1432 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Iaeng Transactions On Engineering Sciences: Special Issue For The International Association Of Engineers Conferences 2014

Author : Sio-iong Ao
Publisher : World Scientific
ISBN 13 : 9814667374
Total Pages : 523 pages
Book Rating : 4.8/5 (146 download)

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Book Synopsis Iaeng Transactions On Engineering Sciences: Special Issue For The International Association Of Engineers Conferences 2014 by : Sio-iong Ao

Download or read book Iaeng Transactions On Engineering Sciences: Special Issue For The International Association Of Engineers Conferences 2014 written by Sio-iong Ao and published by World Scientific. This book was released on 2015-03-11 with total page 523 pages. Available in PDF, EPUB and Kindle. Book excerpt: Two large international conferences on Advances in Engineering Sciences were held in Hong Kong, March 12-14, 2014, under the International MultiConference of Engineers and Computer Scientists (IMECS 2014), and in London, UK, 2-4 July, 2014, under the World Congress on Engineering 2014 (WCE 2014) respectively. This volume contains 37 revised and extended research articles written by prominent researchers participating in the conferences. Topics covered include engineering mathematics, computer science, electrical engineering, manufacturing engineering, industrial engineering, and industrial applications. The book offers tremendous state-of-the-art advances in engineering sciences and also serves as an excellent reference work for researchers and graduate students working with/on engineering sciences.

Issues in Calculus, Mathematical Analysis, and Nonlinear Research: 2013 Edition

Author :
Publisher : ScholarlyEditions
ISBN 13 : 1490111425
Total Pages : 1198 pages
Book Rating : 4.4/5 (91 download)

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Book Synopsis Issues in Calculus, Mathematical Analysis, and Nonlinear Research: 2013 Edition by :

Download or read book Issues in Calculus, Mathematical Analysis, and Nonlinear Research: 2013 Edition written by and published by ScholarlyEditions. This book was released on 2013-05-01 with total page 1198 pages. Available in PDF, EPUB and Kindle. Book excerpt: Issues in Calculus, Mathematical Analysis, and Nonlinear Research: 2013 Edition is a ScholarlyEditions™ book that delivers timely, authoritative, and comprehensive information about Mathematical Analysis. The editors have built Issues in Calculus, Mathematical Analysis, and Nonlinear Research: 2013 Edition on the vast information databases of ScholarlyNews.™ You can expect the information about Mathematical Analysis in this book to be deeper than what you can access anywhere else, as well as consistently reliable, authoritative, informed, and relevant. The content of Issues in Calculus, Mathematical Analysis, and Nonlinear Research: 2013 Edition has been produced by the world’s leading scientists, engineers, analysts, research institutions, and companies. All of the content is from peer-reviewed sources, and all of it is written, assembled, and edited by the editors at ScholarlyEditions™ and available exclusively from us. You now have a source you can cite with authority, confidence, and credibility. More information is available at http://www.ScholarlyEditions.com/.

Nonlinear Analysis

Author : Qamrul Hasan Ansari
Publisher : Springer
ISBN 13 : 8132218833
Total Pages : 362 pages
Book Rating : 4.1/5 (322 download)

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Book Synopsis Nonlinear Analysis by : Qamrul Hasan Ansari

Download or read book Nonlinear Analysis written by Qamrul Hasan Ansari and published by Springer. This book was released on 2014-06-05 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many of our daily-life problems can be written in the form of an optimization problem. Therefore, solution methods are needed to solve such problems. Due to the complexity of the problems, it is not always easy to find the exact solution. However, approximate solutions can be found. The theory of the best approximation is applicable in a variety of problems arising in nonlinear functional analysis and optimization. This book highlights interesting aspects of nonlinear analysis and optimization together with many applications in the areas of physical and social sciences including engineering. It is immensely helpful for young graduates and researchers who are pursuing research in this field, as it provides abundant research resources for researchers and post-doctoral fellows. This will be a valuable addition to the library of anyone who works in the field of applied mathematics, economics and engineering.

Recent Developments in Optimization Theory and Nonlinear Analysis

Author : Yair Censor
Publisher : American Mathematical Soc.
ISBN 13 : 0821805150
Total Pages : 290 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Recent Developments in Optimization Theory and Nonlinear Analysis by : Yair Censor

Download or read book Recent Developments in Optimization Theory and Nonlinear Analysis written by Yair Censor and published by American Mathematical Soc.. This book was released on 1997 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the refereed proceedings of the special session on Optimization and Nonlinear Analysis held at the Joint American Mathematical Society-Israel Mathematical Union Meeting which took place at the Hebrew University of Jerusalem in May 1995. Most of the papers in this book originated from the lectures delivered at this special session. In addition, some participants who didn't present lectures and invited speakers who were unable to attend contributed their work. The fields of optimization theory and nonlinear analysis continue to be very active. This book presents not only the wide spectrum and diversity of the results, but also their manifold connections to other areas, such as differential equations, functional analysis, operator theory, calculus of variations, numerical analysis, and mathematical programming. In reading this book one encounters papers that deal, for example, with convex, quasiconvex and generalized convex functions, fixed and periodic points, fractional-linear transformations, moduli of convexity, monontone operators, Morse lemmas, Navier-Stokes equations, nonexpansive maps, nonsmooth analysis, numerical stability, products of projections, steepest descent, the Leray-Schauder degree, the turnpike property, and variational inequalities.

Control Systems and Mathematical Methods in Economics

Author : Gustav Feichtinger
Publisher : Springer
ISBN 13 : 3319751697
Total Pages : 443 pages
Book Rating : 4.3/5 (197 download)

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Book Synopsis Control Systems and Mathematical Methods in Economics by : Gustav Feichtinger

Download or read book Control Systems and Mathematical Methods in Economics written by Gustav Feichtinger and published by Springer. This book was released on 2018-06-08 with total page 443 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the days of Lev Pontryagin and his associates, the discipline of Optimal Control has enjoyed a tremendous upswing – not only in terms of its mathematical foundations, but also with regard to numerous fields of application, which have given rise to highly active research areas. Few scholars, however, have been able to make contributions to both the mathematical developments and the (socio-)economic applications; Vladimir Veliov is one of them. In the course of his scientific career, he has contributed highly influential research on mathematical aspects of Optimal Control Theory, as well as applications in Economics and Operations Research. One of the hallmarks of his research is its impressive breadth. This volume, published on the occasion of his 65th birthday, accurately reflects that diversity. The mathematical aspects covered include stability theory for difference inclusions, metric regularity, generalized duality theory, the Bolza problem from a functional analytic perspective, and fractional calculus. In turn, the book explores various applications of control theory, such as population dynamics, population economics, epidemiology, optimal growth theory, resource and energy economics, environmental management, and climate change. Further topics include optimal liquidity, dynamics of the firm, and wealth inequality.

Regularization Algorithms for Ill-Posed Problems

Author : Anatoly B. Bakushinsky
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110556383
Total Pages : 447 pages
Book Rating : 4.1/5 (15 download)

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Book Synopsis Regularization Algorithms for Ill-Posed Problems by : Anatoly B. Bakushinsky

Download or read book Regularization Algorithms for Ill-Posed Problems written by Anatoly B. Bakushinsky and published by Walter de Gruyter GmbH & Co KG. This book was released on 2018-02-05 with total page 447 pages. Available in PDF, EPUB and Kindle. Book excerpt: This specialized and authoritative book contains an overview of modern approaches to constructing approximations to solutions of ill-posed operator equations, both linear and nonlinear. These approximation schemes form a basis for implementable numerical algorithms for the stable solution of operator equations arising in contemporary mathematical modeling, and in particular when solving inverse problems of mathematical physics. The book presents in detail stable solution methods for ill-posed problems using the methodology of iterative regularization of classical iterative schemes and the techniques of finite dimensional and finite difference approximations of the problems under study. Special attention is paid to ill-posed Cauchy problems for linear operator differential equations and to ill-posed variational inequalities and optimization problems. The readers are expected to have basic knowledge in functional analysis and differential equations. The book will be of interest to applied mathematicians and specialists in mathematical modeling and inverse problems, and also to advanced students in these fields. Contents Introduction Regularization Methods For Linear Equations Finite Difference Methods Iterative Regularization Methods Finite-Dimensional Iterative Processes Variational Inequalities and Optimization Problems

Multiple Criteria Decision Analysis

Author : Salvatore Greco
Publisher : Springer
ISBN 13 : 149393094X
Total Pages : 1356 pages
Book Rating : 4.4/5 (939 download)

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Book Synopsis Multiple Criteria Decision Analysis by : Salvatore Greco

Download or read book Multiple Criteria Decision Analysis written by Salvatore Greco and published by Springer. This book was released on 2016-02-18 with total page 1356 pages. Available in PDF, EPUB and Kindle. Book excerpt: In two volumes, this new edition presents the state of the art in Multiple Criteria Decision Analysis (MCDA). Reflecting the explosive growth in the field seen during the last several years, the editors not only present surveys of the foundations of MCDA, but look as well at many new areas and new applications. Individual chapter authors are among the most prestigious names in MCDA research, and combined their chapters bring the field completely up to date. Part I of the book considers the history and current state of MCDA, with surveys that cover the early history of MCDA and an overview that discusses the “pre-theoretical” assumptions of MCDA. Part II then presents the foundations of MCDA, with individual chapters that provide a very exhaustive review of preference modeling, along with a chapter devoted to the axiomatic basis of the different models that multiple criteria preferences. Part III looks at outranking methods, with three chapters that consider the ELECTRE methods, PROMETHEE methods, and a look at the rich literature of other outranking methods. Part IV, on Multiattribute Utility and Value Theories (MAUT), presents chapters on the fundamentals of this approach, the very well known UTA methods, the Analytic Hierarchy Process (AHP) and its more recent extension, the Analytic Network Process (ANP), as well as a chapter on MACBETH (Measuring Attractiveness by a Categorical Based Evaluation Technique). Part V looks at Non-Classical MCDA Approaches, with chapters on risk and uncertainty in MCDA, the decision rule approach to MCDA, the fuzzy integral approach, the verbal decision methods, and a tentative assessment of the role of fuzzy sets in decision analysis. Part VI, on Multiobjective Optimization, contains chapters on recent developments of vector and set optimization, the state of the art in continuous multiobjective programming, multiobjective combinatorial optimization, fuzzy multicriteria optimization, a review of the field of goal programming, interactive methods for solving multiobjective optimization problems, and relationships between MCDA and evolutionary multiobjective optimization (EMO). Part VII, on Applications, selects some of the most significant areas, including contributions of MCDA in finance, energy planning problems, telecommunication network planning and design, sustainable development, and portfolio analysis. Finally, Part VIII, on MCDM software, presents well known MCDA software packages.

Handbook of Swarm Intelligence

Author : Bijaya Ketan Panigrahi
Publisher : Springer Science & Business Media
ISBN 13 : 364217390X
Total Pages : 538 pages
Book Rating : 4.6/5 (421 download)

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Book Synopsis Handbook of Swarm Intelligence by : Bijaya Ketan Panigrahi

Download or read book Handbook of Swarm Intelligence written by Bijaya Ketan Panigrahi and published by Springer Science & Business Media. This book was released on 2011-02-04 with total page 538 pages. Available in PDF, EPUB and Kindle. Book excerpt: From nature, we observe swarming behavior in the form of ant colonies, bird flocking, animal herding, honey bees, swarming of bacteria, and many more. It is only in recent years that researchers have taken notice of such natural swarming systems as culmination of some form of innate collective intelligence, albeit swarm intelligence (SI) - a metaphor that inspires a myriad of computational problem-solving techniques. In computational intelligence, swarm-like algorithms have been successfully applied to solve many real-world problems in engineering and sciences. This handbook volume serves as a useful foundational as well as consolidatory state-of-art collection of articles in the field from various researchers around the globe. It has a rich collection of contributions pertaining to the theoretical and empirical study of single and multi-objective variants of swarm intelligence based algorithms like particle swarm optimization (PSO), ant colony optimization (ACO), bacterial foraging optimization algorithm (BFOA), honey bee social foraging algorithms, and harmony search (HS). With chapters describing various applications of SI techniques in real-world engineering problems, this handbook can be a valuable resource for researchers and practitioners, giving an in-depth flavor of what SI is capable of achieving.

Computational Methods In Nonlinear Analysis: Efficient Algorithms, Fixed Point Theory And Applications

Author : Ioannis K Argyros
Publisher : World Scientific
ISBN 13 : 9814405841
Total Pages : 592 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Computational Methods In Nonlinear Analysis: Efficient Algorithms, Fixed Point Theory And Applications by : Ioannis K Argyros

Download or read book Computational Methods In Nonlinear Analysis: Efficient Algorithms, Fixed Point Theory And Applications written by Ioannis K Argyros and published by World Scientific. This book was released on 2013-07-11 with total page 592 pages. Available in PDF, EPUB and Kindle. Book excerpt: The field of computational sciences has seen a considerable development in mathematics, engineering sciences, and economic equilibrium theory. Researchers in this field are faced with the problem of solving a variety of equations or variational inequalities. We note that in computational sciences, the practice of numerical analysis for finding such solutions is essentially connected to variants of Newton's method. The efficient computational methods for finding the solutions of fixed point problems, nonlinear equations and variational inclusions are the first goal of the present book. The second goal is the applications of these methods in nonlinear problems and the connection with fixed point theory.This book is intended for researchers in computational sciences, and as a reference book for an advanced computational methods in nonlinear analysis. We collect the recent results on the convergence analysis of numerical algorithms in both finite-dimensional and infinite-dimensional spaces, and present several applications and connections with fixed point theory. The book contains abundant and updated bibliography, and provides comparison between various investigations made in recent years in the field of computational nonlinear analysis.