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Nonlinear Differential Problems With Smooth And Nonsmooth Constraints

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Nonlinear Differential Problems with Smooth and Nonsmooth Constraints

Nonlinear Differential Problems with Smooth and Nonsmooth Constraints Book
Author : Dumitru Motreanu
Publisher : Academic Press
Release : 2018-02-05
ISBN : 0128133937
Language : En, Es, Fr & De

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Book Description :

Nonlinear Differential Problems with Smooth and Nonsmooth Constraints systematically evaluates how to solve boundary value problems with smooth and nonsmooth constraints. Primarily covering nonlinear elliptic eigenvalue problems and quasilinear elliptic problems using techniques amalgamated from a range of sophisticated nonlinear analysis domains, the work is suitable for PhD and other early career researchers seeking solutions to nonlinear differential equations. Although an advanced work, the book is self-contained, requiring only graduate-level knowledge of functional analysis and topology. Whenever suitable, open problems are stated and partial solutions proposed. The work is accompanied by end-of-chapter problems and carefully curated references. Builds from functional analysis and operator theory, to nonlinear elliptic systems and control problems Outlines the evolution of the main ideas of nonlinear analysis and their roots in classical mathematics Presented with numerous end-of-chapter exercises and sophisticated open problems Illustrated with pertinent industrial and engineering numerical examples and applications Accompanied by hundreds of curated references, saving readers hours of research in conducting literature analysis

Problems of Nonlinear Mechanics and Physics of Materials

Problems of Nonlinear Mechanics and Physics of Materials Book
Author : Igor V. Andrianov,Arkadiy I. Manevich,Yuri V. Mikhlin,Oleg V. Gendelman
Publisher : Springer
Release : 2018-07-31
ISBN : 3319922343
Language : En, Es, Fr & De

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Book Description :

This book presents contributions on the current problems in a number of topical areas of nonlinear dynamics and physics, written by experts from Russia, Ukraine, Israel, Germany, Poland, Italy, the Netherlands, the USA, and France. The book is dedicated to Professor Leonid I. Manevitch, an outstanding scholar in the fields of Mechanics of Solids, Nonlinear Dynamics, and Polymer Physics, on the occasion of his 80th birthday.

Nonsmooth Approach to Optimization Problems with Equilibrium Constraints

Nonsmooth Approach to Optimization Problems with Equilibrium Constraints Book
Author : Jiri Outrata,M. Kocvara,J. Zowe
Publisher : Springer Science & Business Media
Release : 2013-06-29
ISBN : 1475728255
Language : En, Es, Fr & De

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Book Description :

In the early fifties, applied mathematicians, engineers and economists started to pay c10se attention to the optimization problems in which another (lower-Ievel) optimization problem arises as a side constraint. One of the motivating factors was the concept of the Stackelberg solution in game theory, together with its economic applications. Other problems have been encountered in the seventies in natural sciences and engineering. Many of them are of practical importance and have been extensively studied, mainly from the theoretical point of view. Later, applications to mechanics and network design have lead to an extension of the problem formulation: Constraints in form of variation al inequalities and complementarity problems were also admitted. The term "generalized bi level programming problems" was used at first but later, probably in Harker and Pang, 1988, a different terminology was introduced: Mathematical programs with equilibrium constraints, or simply, MPECs. In this book we adhere to MPEC terminology. A large number of papers deals with MPECs but, to our knowledge, there is only one monograph (Luo et al. , 1997). This monograph concentrates on optimality conditions and numerical methods. Our book is oriented similarly, but we focus on those MPECs which can be treated by the implicit programming approach: the equilibrium constraint locally defines a certain implicit function and allows to convert the problem into a mathematical program with a nonsmooth objective.

Numerical Methods for Nonlinear Partial Differential Equations

Numerical Methods for Nonlinear Partial Differential Equations Book
Author : Sören Bartels
Publisher : Springer
Release : 2015-01-19
ISBN : 3319137972
Language : En, Es, Fr & De

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Book Description :

The description of many interesting phenomena in science and engineering leads to infinite-dimensional minimization or evolution problems that define nonlinear partial differential equations. While the development and analysis of numerical methods for linear partial differential equations is nearly complete, only few results are available in the case of nonlinear equations. This monograph devises numerical methods for nonlinear model problems arising in the mathematical description of phase transitions, large bending problems, image processing, and inelastic material behavior. For each of these problems the underlying mathematical model is discussed, the essential analytical properties are explained, and the proposed numerical method is rigorously analyzed. The practicality of the algorithms is illustrated by means of short implementations.

Nonlinear Equations and Spectral Theory

Nonlinear Equations and Spectral Theory Book
Author : M. S. Birman,Nina Nikolaevna Uraltseva
Publisher : American Mathematical Soc.
Release : 2021-07-30
ISBN : 9780821890745
Language : En, Es, Fr & De

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Book Description :

Download Nonlinear Equations and Spectral Theory book written by M. S. Birman,Nina Nikolaevna Uraltseva, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

World Congress of Nonlinear Analysts 92

World Congress of Nonlinear Analysts  92 Book
Author : V. Lakshmikantham
Publisher : Walter de Gruyter
Release : 1996-01-01
ISBN : 3110883236
Language : En, Es, Fr & De

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Book Description :

Download World Congress of Nonlinear Analysts 92 book written by V. Lakshmikantham, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Advanced Topics in Nonsmooth Dynamics

Advanced Topics in Nonsmooth Dynamics Book
Author : Remco Leine,Vincent Acary,Olivier Brüls
Publisher : Springer
Release : 2018-06-07
ISBN : 3319759728
Language : En, Es, Fr & De

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Book Description :

This book discusses emerging topics in the area of nonsmooth dynamics research, such as numerical methods for nonsmooth systems, impact laws for multi-collisions, nonlinear vibrations and control of nonsmooth systems. It documents original work of researchers at the European Network for NonSmooth Dynamics (ENNSD), which provides a cooperation platform for researchers in the field and promotes research focused on nonsmooth dynamics and its applications. Since the establishment of the network in 2012, six ENNSD symposia have been organized at different European locations. The network brings together 40 specialists from 9 different countries in and outside Europe and a wealth of scientific knowledge has been gathered and developed by this group of experts in recent years. The book is of interest to both new and experienced researchers in the field of nonsmooth dynamics. Each chapter is written in such a way as to provide an introduction to the topic for researchers from other fields.

Nonsmooth Critical Point Theory and Nonlinear Boundary Value Problems

Nonsmooth Critical Point Theory and Nonlinear Boundary Value Problems Book
Author : Leszek Gasinski,Nikolaos S. Papageorgiou
Publisher : CRC Press
Release : 2004-07-27
ISBN : 9781420035032
Language : En, Es, Fr & De

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Book Description :

Starting in the early 1980s, people using the tools of nonsmooth analysis developed some remarkable nonsmooth extensions of the existing critical point theory. Until now, however, no one had gathered these tools and results together into a unified, systematic survey of these advances. This book fills that gap. It provides a complete presentation of nonsmooth critical point theory, then goes beyond it to study nonlinear second order boundary value problems. The authors do not limit their treatment to problems in variational form. They also examine in detail equations driven by the p-Laplacian, its generalizations, and their spectral properties, studying a wide variety of problems and illustrating the powerful tools of modern nonlinear analysis. The presentation includes many recent results, including some that were previously unpublished. Detailed appendices outline the fundamental mathematical tools used in the book, and a rich bibliography forms a guide to the relevant literature. Most books addressing critical point theory deal only with smooth problems, linear or semilinear problems, or consider only variational methods or the tools of nonlinear operators. Nonsmooth Critical Point Theory and Nonlinear Boundary Value Problems offers a comprehensive treatment of the subject that is up-to-date, self-contained, and rich in methods for a wide variety of problems.

Optimal Control Via Nonsmooth Analysis

Optimal Control Via Nonsmooth Analysis Book
Author : Philip Daniel Loewen
Publisher : American Mathematical Soc.
Release : 1993
ISBN : 9780821869963
Language : En, Es, Fr & De

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Book Description :

This book provides a complete and unified treatment of deterministic problems of dynamic optimization, from the classical themes of the calculus of variations to the forefront of modern research in optimal control. At the heart of the presentation is nonsmooth analysis, a theory of local approximation developed over the last twenty years to provide useful first-order information about sets and functions lying beyond the reach of classical analysis. The book includes an intuitive and geometrically transparent approach to nonsmooth analysis, serving not only to introduce the basic ideas, but also to illuminate the calculations and derivations in the applied sections dealing with the calculus of variations and optimal control. Written in a lively, engaging style and stocked with numerous figures and practice problems, this book offers an ideal introduction to this vigorous field of current research. It is suitable as a graduate text for a one-semester course in optimal control or as a manual for self-study. Each chapter closes with a list of references to ease the reader's transition from active learner to contributing researcher.

Nonlinear Analysis Differential Equations and Control

Nonlinear Analysis  Differential Equations and Control Book
Author : F.H. Clarke,R.J. Stern
Publisher : Springer Science & Business Media
Release : 2012-12-06
ISBN : 9401145601
Language : En, Es, Fr & De

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Book Description :

Recent years have witnessed important developments in those areas of the mathematical sciences where the basic model under study is a dynamical system such as a differential equation or control process. Many of these recent advances were made possible by parallel developments in nonlinear and nonsmooth analysis. The latter subjects, in general terms, encompass differential analysis and optimization theory in the absence of traditional linearity, convexity or smoothness assumptions. In the last three decades it has become increasingly recognized that nonlinear and nonsmooth behavior is naturally present and prevalent in dynamical models, and is therefore significant theoretically. This point of view has guided us in the organizational aspects of this ASI. Our goals were twofold: We intended to achieve "cross fertilization" between mathematicians who were working in a diverse range of problem areas, but who all shared an interest in nonlinear and nonsmooth analysis. More importantly, it was our goal to expose a young international audience (mainly graduate students and recent Ph. D. 's) to these important subjects. In that regard, there were heavy pedagogical demands placed upon the twelve speakers of the ASI, in meeting the needs of such a gathering. The talks, while exposing current areas of research activity, were required to be as introductory and comprehensive as possible. It is our belief that these goals were achieved, and that these proceedings bear this out. Each of the twelve speakers presented a mini-course of four or five hours duration.

Neural Information Processing

Neural Information Processing Book
Author : Irwin King,Jun Wang,Laiwan Chan,DeLiang Wang
Publisher : Springer Science & Business Media
Release : 2006-09-26
ISBN : 3540464816
Language : En, Es, Fr & De

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Book Description :

The three volume set LNCS 4232, LNCS 4233, and LNCS 4234 constitutes the refereed proceedings of the 13th International Conference on Neural Information Processing, ICONIP 2006, held in Hong Kong, China in October 2006. The 386 revised full papers presented were carefully reviewed and selected from 1175 submissions.

Nonlinear Equations and Optimisation

Nonlinear Equations and Optimisation Book
Author : L.T. Watson,J.A. Ford,M. Bartholomew-Biggs
Publisher : Elsevier
Release : 2001-03-14
ISBN : 0080929540
Language : En, Es, Fr & De

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Book Description :

/homepage/sac/cam/na2000/index.html7-Volume Set now available at special set price ! In one of the papers in this collection, the remark that "nothing at all takes place in the universe in which some rule of maximum of minimum does not appear" is attributed to no less an authority than Euler. Simplifying the syntax a little, we might paraphrase this as Everything is an optimization problem. While this might be something of an overstatement, the element of exaggeration is certainly reduced if we consider the extended form: Everything is an optimization problem or a system of equations. This observation, even if only partly true, stands as a fitting testimonial to the importance of the work covered by this volume. Since the 1960s, much effort has gone into the development and application of numerical algorithms for solving problems in the two areas of optimization and systems of equations. As a result, many different ideas have been proposed for dealing efficiently with (for example) severe nonlinearities and/or very large numbers of variables. Libraries of powerful software now embody the most successful of these ideas, and one objective of this volume is to assist potential users in choosing appropriate software for the problems they need to solve. More generally, however, these collected review articles are intended to provide both researchers and practitioners with snapshots of the 'state-of-the-art' with regard to algorithms for particular classes of problem. These snapshots are meant to have the virtues of immediacy through the inclusion of very recent ideas, but they also have sufficient depth of field to show how ideas have developed and how today's research questions have grown out of previous solution attempts. The most efficient methods for local optimization, both unconstrained and constrained, are still derived from the classical Newton approach. As well as dealing in depth with the various classical, or neo-classical, approaches, the selection of papers on optimization in this volume ensures that newer ideas are also well represented. Solving nonlinear algebraic systems of equations is closely related to optimization. The two are not completely equivalent, however, and usually something is lost in the translation. Algorithms for nonlinear equations can be roughly classified as locally convergent or globally convergent. The characterization is not perfect. Locally convergent algorithms include Newton's method, modern quasi-Newton variants of Newton's method, and trust region methods. All of these approaches are well represented in this volume.

Recent Trends in Nonlinear Partial Differential Equations

Recent Trends in Nonlinear Partial Differential Equations Book
Author : Patrizia Pucci
Publisher : American Mathematical Soc.
Release : 2013
ISBN : 0821898612
Language : En, Es, Fr & De

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Book Description :

This book is the second of two volumes that contain the proceedings of the Workshop on Nonlinear Partial Differential Equations, held from May 28-June 1, 2012, at the University of Perugia in honor of Patrizia Pucci's 60th birthday. The workshop brought together leading experts and researchers in nonlinear partial differential equations to promote research and to stimulate interactions among the participants. The workshop program testified to the wide ranging influence of Patrizia Pucci on the field of nonlinear analysis and partial differential equations. In her own work, Patrizia Pucci has been a seminal influence in many important areas: the maximum principle, qualitative analysis of solutions to many classes of nonlinear PDEs (Kirchhoff problems, polyharmonic systems), mountain pass theorem in the critical case, critical exponents, variational identities, as well as various degenerate or singular phenomena in mathematical physics. This same breadth is reflected in the mathematical papers included in this volume. The companion volume (Contemporary Mathematics, Volume 594) is devoted to evolution problems in nonlinear partial differential equations.

Applied Non Linear Dynamical Systems

Applied Non Linear Dynamical Systems Book
Author : Jan Awrejcewicz
Publisher : Springer
Release : 2014-10-21
ISBN : 3319082663
Language : En, Es, Fr & De

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Book Description :

The book is a collection of contributions devoted to analytical, numerical and experimental techniques of dynamical systems, presented at the International Conference on Dynamical Systems: Theory and Applications, held in Łódź, Poland on December 2-5, 2013. The studies give deep insight into both the theory and applications of non-linear dynamical systems, emphasizing directions for future research. Topics covered include: constrained motion of mechanical systems and tracking control; diversities in the inverse dynamics; singularly perturbed ODEs with periodic coefficients; asymptotic solutions to the problem of vortex structure around a cylinder; investigation of the regular and chaotic dynamics; rare phenomena and chaos in power converters; non-holonomic constraints in wheeled robots; exotic bifurcations in non-smooth systems; micro-chaos; energy exchange of coupled oscillators; HIV dynamics; homogenous transformations with applications to off-shore slender structures; novel approaches to a qualitative study of a dissipative system; chaos of postural sway in humans; oscillators with fractional derivatives; controlling chaos via bifurcation diagrams; theories relating to optical choppers with rotating wheels; dynamics in expert systems; shooting methods for non-standard boundary value problems; automatic sleep scoring governed by delay differential equations; isochronous oscillations; the aerodynamics pendulum and its limit cycles; constrained N-body problems; nano-fractal oscillators and dynamically-coupled dry friction.

Cloud Computing for Optimization Foundations Applications and Challenges

Cloud Computing for Optimization  Foundations  Applications  and Challenges Book
Author : Bhabani Shankar Prasad Mishra,Himansu Das,Satchidananda Dehuri,Alok Kumar Jagadev
Publisher : Springer
Release : 2018-02-26
ISBN : 3319736760
Language : En, Es, Fr & De

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Book Description :

This book discusses harnessing the real power of cloud computing in optimization problems, presenting state-of-the-art computing paradigms, advances in applications, and challenges concerning both the theories and applications of cloud computing in optimization with a focus on diverse fields like the Internet of Things, fog-assisted cloud computing, and big data. In real life, many problems – ranging from social science to engineering sciences – can be identified as complex optimization problems. Very often these are intractable, and as a result researchers from industry as well as the academic community are concentrating their efforts on developing methods of addressing them. Further, the cloud computing paradigm plays a vital role in many areas of interest, like resource allocation, scheduling, energy management, virtualization, and security, and these areas are intertwined with many optimization problems. Using illustrations and figures, this book offers students and researchers a clear overview of the concepts and practices of cloud computing and its use in numerous complex optimization problems.

Systems with Non Smooth Inputs

Systems with Non Smooth Inputs Book
Author : Jürgen Appell,Nguyen Thi Hien,Lyubov Petrova,Irina Pryadko
Publisher : Walter de Gruyter GmbH & Co KG
Release : 2021-03-22
ISBN : 3110709937
Language : En, Es, Fr & De

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Book Description :

The authors present a completely new and highly application-oriented field of nonlinear analysis. The work covers the theory of non-smooth input-output systems and presents various methods to non-standard applications in mathematics and physics. A particular focus lies on hysteresis and relay phenomena, electric circuits with diode nonlinearities, and biological systems with constraints.

Duality Principles in Nonconvex Systems

Duality Principles in Nonconvex Systems Book
Author : David Yang Gao
Publisher : Springer Science & Business Media
Release : 2013-03-09
ISBN : 1475731760
Language : En, Es, Fr & De

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Book Description :

Motivated by practical problems in engineering and physics, drawing on a wide range of applied mathematical disciplines, this book is the first to provide, within a unified framework, a self-contained comprehensive mathematical theory of duality for general non-convex, non-smooth systems, with emphasis on methods and applications in engineering mechanics. Topics covered include the classical (minimax) mono-duality of convex static equilibria, the beautiful bi-duality in dynamical systems, the interesting tri-duality in non-convex problems and the complicated multi-duality in general canonical systems. A potentially powerful sequential canonical dual transformation method for solving fully nonlinear problems is developed heuristically and illustrated by use of many interesting examples as well as extensive applications in a wide variety of nonlinear systems, including differential equations, variational problems and inequalities, constrained global optimization, multi-well phase transitions, non-smooth post-bifurcation, large deformation mechanics, structural limit analysis, differential geometry and non-convex dynamical systems. With exceptionally coherent and lucid exposition, the work fills a big gap between the mathematical and engineering sciences. It shows how to use formal language and duality methods to model natural phenomena, to construct intrinsic frameworks in different fields and to provide ideas, concepts and powerful methods for solving non-convex, non-smooth problems arising naturally in engineering and science. Much of the book contains material that is new, both in its manner of presentation and in its research development. A self-contained appendix provides some necessary background from elementary functional analysis. Audience: The book will be a valuable resource for students and researchers in applied mathematics, physics, mechanics and engineering. The whole volume or selected chapters can also be recommended as a text for both senior undergraduate and graduate courses in applied mathematics, mechanics, general engineering science and other areas in which the notions of optimization and variational methods are employed.

Proceedings of the Thirteenth International Conference on Management Science and Engineering Management

Proceedings of the Thirteenth International Conference on Management Science and Engineering Management Book
Author : Jiuping Xu,Syed Ejaz Ahmed,Fang Lee Cooke,Gheorghe Duca
Publisher : Springer
Release : 2019-06-19
ISBN : 3030212483
Language : En, Es, Fr & De

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Book Description :

This book gathers the proceedings of the 13th International Conference on Management Science and Engineering Management (ICMSEM 2019), which was held at Brock University, Ontario, Canada on August 5–8, 2019. Exploring the latest ideas and pioneering research achievements in management science and engineering management, the respective contributions highlight both theoretical and practical studies on management science and computing methodologies, and present advanced management concepts and computing technologies for decision-making problems involving large, uncertain and unstructured data. Accordingly, the proceedings offer researchers and practitioners in related fields an essential update, as well as a source of new research directions.

Large Scale Optimization

Large Scale Optimization Book
Author : William W. Hager,D.W. Hearn,Panos M. Pardalos
Publisher : Springer Science & Business Media
Release : 2013-12-01
ISBN : 1461336325
Language : En, Es, Fr & De

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Book Description :

On February 15-17, 1993, a conference on Large Scale Optimization, hosted by the Center for Applied Optimization, was held at the University of Florida. The con ference was supported by the National Science Foundation, the U. S. Army Research Office, and the University of Florida, with endorsements from SIAM, MPS, ORSA and IMACS. Forty one invited speakers presented papers on mathematical program ming and optimal control topics with an emphasis on algorithm development, real world applications and numerical results. Participants from Canada, Japan, Sweden, The Netherlands, Germany, Belgium, Greece, and Denmark gave the meeting an important international component. At tendees also included representatives from IBM, American Airlines, US Air, United Parcel Serice, AT & T Bell Labs, Thinking Machines, Army High Performance Com puting Research Center, and Argonne National Laboratory. In addition, the NSF sponsored attendance of thirteen graduate students from universities in the United States and abroad. Accurate modeling of scientific problems often leads to the formulation of large scale optimization problems involving thousands of continuous and/or discrete vari ables. Large scale optimization has seen a dramatic increase in activities in the past decade. This has been a natural consequence of new algorithmic developments and of the increased power of computers. For example, decomposition ideas proposed by G. Dantzig and P. Wolfe in the 1960's, are now implement able in distributed process ing systems, and today many optimization codes have been implemented on parallel machines.

Nonlinear Optimization and Related Topics

Nonlinear Optimization and Related Topics Book
Author : Gianni Pillo,F. Giannessi
Publisher : Springer Science & Business Media
Release : 2013-06-29
ISBN : 1475732260
Language : En, Es, Fr & De

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Book Description :

This volume contains the edited texts of the lectures presented at the Workshop on Nonlinear Optimization held in Erice, Sicily, at the "G. Stampacchia" School of Mathematics of the "E. Majorana" Centre for Scientific Culture, June 23 -July 2, 1998. In the tradition of these meetings, the main purpose was to review and discuss recent advances and promising research trends concerning theory, algorithms and innovative applications in the field of Nonlinear Optimization, and of related topics such as Convex Optimization, Nonsmooth Optimization, Variational Inequalities and Complementarity Problems. The meeting was attended by 83 people from 21 countries. Besides the lectures, several formal and informal discussions took place. The result was a wide and deep knowledge of the present research tendencies in the field. We wish to express our appreciation for the active contribution of all the par ticipants in the meeting. Our gratitude is due to the Ettore Majorana Centre in Erice, which offered its facilities and rewarding environment: its staff was certainly instrumental for the success of the meeting. Our gratitude is also due to Francisco Facchinei and Massimo Roma for the effort and time devoted as members of the Organising Committee. We are indebted to the Italian National Research Council, and in particular to the Group on Functional Analysis and its Applications and to the Committees on Engineering Sciences and on Information Sciences and Technolo gies for their financial support. Finally, we address our thanks to Kluwer Academic Publishers for having offered to publish this volume.