Nonlinear Differential Problems With Smooth And Nonsmooth Constraints PDF Download
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| Author | : Dumitru Motreanu |
| Publisher | : Academic Press |
| Total Pages | : 364 |
| Release | : 2018-02-05 |
| Genre | : Mathematics |
| ISBN | : 0128133937 |
Download Nonlinear Differential Problems with Smooth and Nonsmooth Constraints Book in PDF, ePub and Kindle
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
| Author | : Jiri Outrata |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 300 |
| Release | : 1998-07-31 |
| Genre | : Business & Economics |
| ISBN | : 0792351703 |
Download Nonsmooth Approach to Optimization Problems with Equilibrium Constraints Book in PDF, ePub and Kindle
This book presents an in-depth study and a solution technique for an important class of optimization problems. This class is characterized by special constraints: parameter-dependent convex programs, variational inequalities or complementarity problems. All these so-called equilibrium constraints are mostly treated in a convenient form of generalized equations. The book begins with a chapter on auxiliary results followed by a description of the main numerical tools: a bundle method of nonsmooth optimization and a nonsmooth variant of Newton's method. Following this, stability and sensitivity theory for generalized equations is presented, based on the concept of strong regularity. This enables one to apply the generalized differential calculus for Lipschitz maps to derive optimality conditions and to arrive at a solution method. A large part of the book focuses on applications coming from continuum mechanics and mathematical economy. A series of nonacademic problems is introduced and analyzed in detail. Each problem is accompanied with examples that show the efficiency of the solution method. This book is addressed to applied mathematicians and engineers working in continuum mechanics, operations research and economic modelling. Students interested in optimization will also find the book useful.
| Author | : Marius Durea |
| Publisher | : Walter de Gruyter GmbH & Co KG |
| Total Pages | : 328 |
| Release | : 2014-12-15 |
| Genre | : Mathematics |
| ISBN | : 3110426048 |
Download An Introduction to Nonlinear Optimization Theory Book in PDF, ePub and Kindle
The goal of this book is to present the main ideas and techniques in the field of continuous smooth and nonsmooth optimization. Starting with the case of differentiable data and the classical results on constrained optimization problems, and continuing with the topic of nonsmooth objects involved in optimization theory, the book concentrates on both theoretical and practical aspects of this field. This book prepares those who are engaged in research by giving repeated insights into ideas that are subsequently dealt with and illustrated in detail.
| Author | : Jorge Nocedal |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 686 |
| Release | : 2006-12-11 |
| Genre | : Mathematics |
| ISBN | : 0387400656 |
Download Numerical Optimization Book in PDF, ePub and Kindle
Optimization is an important tool used in decision science and for the analysis of physical systems used in engineering. One can trace its roots to the Calculus of Variations and the work of Euler and Lagrange. This natural and reasonable approach to mathematical programming covers numerical methods for finite-dimensional optimization problems. It begins with very simple ideas progressing through more complicated concepts, concentrating on methods for both unconstrained and constrained optimization.
| Author | : Vincent Acary |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 529 |
| Release | : 2008-01-30 |
| Genre | : Technology & Engineering |
| ISBN | : 3540753923 |
Download Numerical Methods for Nonsmooth Dynamical Systems Book in PDF, ePub and Kindle
This book concerns the numerical simulation of dynamical systems whose trajec- ries may not be differentiable everywhere. They are named nonsmooth dynamical systems. They make an important class of systems, rst because of the many app- cations in which nonsmooth models are useful, secondly because they give rise to new problems in various elds of science. Usually nonsmooth dynamical systems are represented as differential inclusions, complementarity systems, evolution va- ational inequalities, each of these classes itself being split into several subclasses. The book is divided into four parts, the rst three parts being sketched in Fig. 0. 1. The aim of the rst part is to present the main tools from mechanics and applied mathematics which are necessary to understand how nonsmooth dynamical systems may be numerically simulated in a reliable way. Many examples illustrate the th- retical results, and an emphasis is put on mechanical systems, as well as on electrical circuits (the so-called Filippov’s systems are also examined in some detail, due to their importance in control applications). The second and third parts are dedicated to a detailed presentation of the numerical schemes. A fourth part is devoted to the presentation of the software platform Siconos. This book is not a textbook on - merical analysis of nonsmooth systems, in the sense that despite the main results of numerical analysis (convergence, order of consistency, etc. ) being presented, their proofs are not provided.
| Author | : Michael Hintermüller |
| Publisher | : Springer Nature |
| Total Pages | : 518 |
| Release | : 2022-02-18 |
| Genre | : Mathematics |
| ISBN | : 3030793931 |
Download Non-Smooth and Complementarity-Based Distributed Parameter Systems Book in PDF, ePub and Kindle
Many of the most challenging problems in the applied sciences involve non-differentiable structures as well as partial differential operators, thus leading to non-smooth distributed parameter systems. This edited volume aims to establish a theoretical and numerical foundation and develop new algorithmic paradigms for the treatment of non-smooth phenomena and associated parameter influences. Other goals include the realization and further advancement of these concepts in the context of robust and hierarchical optimization, partial differential games, and nonlinear partial differential complementarity problems, as well as their validation in the context of complex applications. Areas for which applications are considered include optimal control of multiphase fluids and of superconductors, image processing, thermoforming, and the formation of rivers and networks. Chapters are written by leading researchers and present results obtained in the first funding phase of the DFG Special Priority Program on Nonsmooth and Complementarity Based Distributed Parameter Systems: Simulation and Hierarchical Optimization that ran from 2016 to 2019.
| Author | : Giorgio Giorgi |
| Publisher | : Elsevier |
| Total Pages | : 615 |
| Release | : 2004-03-10 |
| Genre | : Mathematics |
| ISBN | : 008053595X |
Download Mathematics of Optimization: Smooth and Nonsmooth Case Book in PDF, ePub and Kindle
The book is intended for people (graduates, researchers, but also undergraduates with a good mathematical background) involved in the study of (static) optimization problems (in finite-dimensional spaces). It contains a lot of material, from basic tools of convex analysis to optimality conditions for smooth optimization problems, for non smooth optimization problems and for vector optimization problems.The development of the subjects are self-contained and the bibliographical references are usually treated in different books (only a few books on optimization theory deal also with vector problems), so the book can be a starting point for further readings in a more specialized literature.Assuming only a good (even if not advanced) knowledge of mathematical analysis and linear algebra, this book presents various aspects of the mathematical theory in optimization problems. The treatment is performed in finite-dimensional spaces and with no regard to algorithmic questions. After two chapters concerning, respectively, introductory subjects and basic tools and concepts of convex analysis, the book treats extensively mathematical programming problems in the smmoth case, in the nonsmooth case and finally vector optimization problems. · Self-contained· Clear style and results are either proved or stated precisely with adequate references· The authors have several years experience in this field· Several subjects (some of them non usual in books of this kind) in one single book, including nonsmooth optimization and vector optimization problems· Useful long references list at the end of each chapter
| Author | : Dumitru Motreanu |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 384 |
| Release | : 2013-06-29 |
| Genre | : Mathematics |
| ISBN | : 1475769210 |
Download Variational and Non-variational Methods in Nonlinear Analysis and Boundary Value Problems Book in PDF, ePub and Kindle
This book reflects a significant part of authors' research activity dur ing the last ten years. The present monograph is constructed on the results obtained by the authors through their direct cooperation or due to the authors separately or in cooperation with other mathematicians. All these results fit in a unitary scheme giving the structure of this work. The book is mainly addressed to researchers and scholars in Pure and Applied Mathematics, Mechanics, Physics and Engineering. We are greatly indebted to Viorica Venera Motreanu for the careful reading of the manuscript and helpful comments on important issues. We are also grateful to our Editors of Kluwer Academic Publishers for their professional assistance. Our deepest thanks go to our numerous scientific collaborators and friends, whose work was so important for us. D. Motreanu and V. Radulescu IX Introduction The present monograph is based on original results obtained by the authors in the last decade. This book provides a comprehensive expo sition of some modern topics in nonlinear analysis with applications to the study of several classes of boundary value problems. Our framework includes multivalued elliptic problems with discontinuities, variational inequalities, hemivariational inequalities and evolution problems. The treatment relies on variational methods, monotonicity principles, topo logical arguments and optimization techniques. Excepting Sections 1 and 3 in Chapter 1 and Sections 1 and 3 in Chapter 2, the material is new in comparison with any other book, representing research topics where the authors contributed. The outline of our work is the following.
| Author | : Valery N. Pilipchuk |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 366 |
| Release | : 2010-05-09 |
| Genre | : Science |
| ISBN | : 3642127991 |
Download Nonlinear Dynamics Book in PDF, ePub and Kindle
Nonlinear Dynamics represents a wide interdisciplinary area of research dealing with a variety of “unusual” physical phenomena by means of nonlinear differential equations, discrete mappings, and related mathematical algorithms. However, with no real substitute for the linear superposition principle, the methods of Nonlinear Dynamics appeared to be very diverse, individual and technically complicated. This book makes an attempt to find a common ground for nonlinear dynamic analyses based on the existence of strongly nonlinear but quite simple counterparts to the linear models and tools. It is shown that, since the subgroup of rotations, harmonic oscillators, and the conventional complex analysis generate linear and weakly nonlinear approaches, then translations and reflections, impact oscillators, and hyperbolic (Clifford’s) algebras must give rise to some “quasi impact” methodology. Such strongly nonlinear methods are developed in several chapters of this book based on the idea of non-smooth time substitutions. Although most of the illustrations are based on mechanical oscillators, the area of applications may include also electric, electro-mechanical, electrochemical and other physical models generating strongly anharmonic temporal signals or spatial distributions. Possible applications to periodic elastic structures with non-smooth or discontinuous characteristics are outlined in the final chapter of the book.
| Author | : Piernicola Bettiol |
| Publisher | : Springer Nature |
| Total Pages | : 789 |
| Release | : |
| Genre | : |
| ISBN | : 303150089X |
Download Principles of Dynamic Optimization Book in PDF, ePub and Kindle
