Analysis and Methods in Nonsmooth and Nonconvex Optimization

Analysis and Methods in Nonsmooth and Nonconvex Optimization

The purpose of this thesis is to propose, by a variety of techniques from nonsmooth and convex analysis, numerical methods for the solution of nonsmooth equations and nonconvex minimization problems arising in mathematical programming, ...

Author: Huifu Xu

Publisher:

ISBN: OCLC:222573925

Category: Nonsmooth optimization

Page: 486

View: 368

The purpose of this thesis is to propose, by a variety of techniques from nonsmooth and convex analysis, numerical methods for the solution of nonsmooth equations and nonconvex minimization problems arising in mathematical programming, economics, engineering, and sciences.
Categories: Nonsmooth optimization

Nonsmooth Nonconvex Mechanics

Nonsmooth Nonconvex Mechanics

This volume contains 22 chapters written by various leading researchers and presents a cohesive and authoritative overview of recent results and applications in the area of nonsmooth and nonconvex mechanics.

Author: David Yang Gao

Publisher: Springer Science & Business Media

ISBN: 9781461302759

Category: Mathematics

Page: 476

View: 946

Nonsmooth and nonconvex models arise in several important applications of mechanics and engineering. The interest in this field is growing from both mathematicians and engineers. The study of numerous industrial applications, including contact phenomena in statics and dynamics or delamination effects in composites, require the consideration of nonsmoothness and nonconvexity. The mathematical topics discussed in this book include variational and hemivariational inequalities, duality, complementarity, variational principles, sensitivity analysis, eigenvalue and resonance problems, and minimax problems. Applications are considered in the following areas among others: nonsmooth statics and dynamics, stability of quasi- static evolution processes, friction problems, adhesive contact and debonding, inverse problems, pseudoelastic modeling of phase transitions, chaotic behavior in nonlinear beams, and nonholonomic mechanical systems. This volume contains 22 chapters written by various leading researchers and presents a cohesive and authoritative overview of recent results and applications in the area of nonsmooth and nonconvex mechanics. Audience: Faculty, graduate students, and researchers in applied mathematics, optimization, control and engineering.
Categories: Mathematics

Convex Analysis and Global Optimization

Convex Analysis and Global Optimization

From the reviews of the first edition: The book gives a good review of the topic. ...The text is carefully constructed and well written, the exposition is clear.

Author: Hoang Tuy

Publisher: Springer

ISBN: 9783319314846

Category: Mathematics

Page: 505

View: 696

This book presents state-of-the-art results and methodologies in modern global optimization, and has been a staple reference for researchers, engineers, advanced students (also in applied mathematics), and practitioners in various fields of engineering. The second edition has been brought up to date and continues to develop a coherent and rigorous theory of deterministic global optimization, highlighting the essential role of convex analysis. The text has been revised and expanded to meet the needs of research, education, and applications for many years to come. Updates for this new edition include: · Discussion of modern approaches to minimax, fixed point, and equilibrium theorems, and to nonconvex optimization; · Increased focus on dealing more efficiently with ill-posed problems of global optimization, particularly those with hard constraints; · Important discussions of decomposition methods for specially structured problems; · A complete revision of the chapter on nonconvex quadratic programming, in order to encompass the advances made in quadratic optimization since publication of the first edition. · Additionally, this new edition contains entirely new chapters devoted to monotonic optimization, polynomial optimization and optimization under equilibrium constraints, including bilevel programming, multiobjective programming, and optimization with variational inequality constraint. From the reviews of the first edition: The book gives a good review of the topic. ...The text is carefully constructed and well written, the exposition is clear. It leaves a remarkable impression of the concepts, tools and techniques in global optimization. It might also be used as a basis and guideline for lectures on this subject. Students as well as professionals will profitably read and use it.—Mathematical Methods of Operations Research, 49:3 (1999)
Categories: Mathematics

Topological Methods in Nonlinear Analysis

Topological Methods in Nonlinear Analysis

( 14 ) A . MARINO AND M . Tosques , Some variational problems with lack of
convexity and some partial differential inequalities , Methods of Nonconvex
Analysis , Proceedings from CIME , Varenna 1989 ( A . Cellina , ed . ) , Springer ,
Berlin ...

Author:

Publisher:

ISBN: UOM:39015055744364

Category: Nonlinear functional analysis

Page:

View: 400

Categories: Nonlinear functional analysis

Abstract Convexity and Global Optimization

Abstract Convexity and Global Optimization

This book consists of two parts.

Author: Alexander M. Rubinov

Publisher: Springer Science & Business Media

ISBN: 079236323X

Category: Mathematics

Page: 490

View: 912

This book consists of two parts. Firstly, the main notions of abstract convexity and their applications in the study of some classes of functions and sets are presented. Secondly, both theoretical and numerical aspects of global optimization based on abstract convexity are examined. Most of the book does not require knowledge of advanced mathematics. Classical methods of nonconvex mathematical programming, being based on a local approximation, cannot be used to examine and solve many problems of global optimization, and so there is a clear need to develop special global tools for solving these problems. Some of these tools are based on abstract convexity, that is, on the representation of a function of a rather complicated nature as the upper envelope of a set of fairly simple functions. Audience: The book will be of interest to specialists in global optimization, mathematical programming, and convex analysis, as well as engineers using mathematical tools and optimization techniques and specialists in mathematical modelling.
Categories: Mathematics

Duality Principles in Nonconvex Systems

Duality Principles in Nonconvex Systems

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 ...

Author: David Yang Gao

Publisher: Springer Science & Business Media

ISBN: 9781475731767

Category: Mathematics

Page: 454

View: 536

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.
Categories: Mathematics

Nonlinear Analysis Theory and Methods

Nonlinear Analysis   Theory and Methods

13, 757–768 (2003) B. Dacorogna, Direct Methods in the Calculus of Variations (
Springer, New York, 1989) G. Dal Maso, ... (NS)1, 443–474 (1979) I. Ekeland,
The ε-variational principle revisited, in Methods of Nonconvex Analysis, Lecture ...

Author: Nikolaos S. Papageorgiou

Publisher: Springer

ISBN: 9783030034306

Category: Mathematics

Page: 577

View: 135

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.
Categories: Mathematics

Finite Element Method for Hemivariational Inequalities

Finite Element Method for Hemivariational Inequalities

Discretized models are numerically treated as nonconvex and nonsmooth optimization problems. The book includes a comprehensive description of typical representants of nonsmooth optimization methods.

Author: J. Haslinger

Publisher: Springer Science & Business Media

ISBN: 9781475752335

Category: Mathematics

Page: 260

View: 582

Hemivariational inequalities represent an important class of problems in nonsmooth and nonconvex mechanics. By means of them, problems with nonmonotone, possibly multivalued, constitutive laws can be formulated, mathematically analyzed and finally numerically solved. The present book gives a rigorous analysis of finite element approximation for a class of hemivariational inequalities of elliptic and parabolic type. Finite element models are described and their convergence properties are established. Discretized models are numerically treated as nonconvex and nonsmooth optimization problems. The book includes a comprehensive description of typical representants of nonsmooth optimization methods. Basic knowledge of finite element mathematics, functional and nonsmooth analysis is needed. The book is self-contained, and all necessary results from these disciplines are summarized in the introductory chapter. Audience: Engineers and applied mathematicians at universities and working in industry. Also graduate-level students in advanced nonlinear computational mechanics, mathematics of finite elements and approximation theory. Chapter 1 includes the necessary prerequisite materials.
Categories: Mathematics

Proceedings of the 1988 American Control Conference

Proceedings of the 1988 American Control Conference

[ FLA76 ] A. V. Fiacco " Sensitivity Analysis for Nonlinear Programming Using
Penalty Method , " Math . ... [ BER79 ] D. P. Bertsekas , " Convexification
Procedure and Decomposition Methods for Nonconvex Optimization Problems , "
JOTA , Vol .

Author:

Publisher:

ISBN: UCSD:31822003643194

Category: Automatic control

Page: 2503

View: 947

Categories: Automatic control

Handbook of Nonconvex Analysis and Applications

Handbook of Nonconvex Analysis and Applications

This Handbook will serve as a much-needed reference work for the dynamic and ever-growing field of nonconvex analysis and its applications.

Author: David Yang Gao

Publisher: International Pressof Boston Incorporated

ISBN: 1571462007

Category: Mathematics

Page: 680

View: 753

Categories: Mathematics

Conjugate Gradient Algorithms in Nonconvex Optimization

Conjugate Gradient Algorithms in Nonconvex Optimization

This book details algorithms for large-scale unconstrained and bound constrained optimization.

Author: Radoslaw Pytlak

Publisher: Springer Science & Business Media

ISBN: 9783540856344

Category: Mathematics

Page: 478

View: 758

This book details algorithms for large-scale unconstrained and bound constrained optimization. It shows optimization techniques from a conjugate gradient algorithm perspective as well as methods of shortest residuals, which have been developed by the author.
Categories: Mathematics

Topological Methods in Complementarity Theory

Topological Methods in Complementarity Theory

The book is dedicated to the study of nonlinear complementarity problems by topological methods.

Author: G. Isac

Publisher: Springer Science & Business Media

ISBN: 0792362748

Category: Business & Economics

Page: 683

View: 216

Complementarity theory is a new domain in applied mathematics and is concerned with the study of complementarity problems. These problems represent a wide class of mathematical models related to optimization, game theory, economic engineering, mechanics, fluid mechanics, stochastic optimal control etc. The book is dedicated to the study of nonlinear complementarity problems by topological methods. Audience: Mathematicians, engineers, economists, specialists working in operations research and anybody interested in applied mathematics or in mathematical modeling.
Categories: Business & Economics

Mathematical Reviews

Mathematical Reviews

Global convergence of the methods can makes them amenable to non - smooth
analysis techniques like be ... bundle methods for non - convex maximum
eigenvalue A feasible trust - region sequential quadratic programming algorithm
 ...

Author:

Publisher:

ISBN: UOM:39015067268402

Category: Mathematics

Page:

View: 605

Categories: Mathematics

International Books in Print

International Books in Print

ne Els ( 620 ) Methods of Functional Analysis in Approximation Theory / ed by
Micchelli , C.A. et al . ... Sz WHO ( 574 : 614 ) Methods of Nonconvex Analysis :
Lectures Given at the 1st Session of the Centro Internazionale Estivo Matematico
 ...

Author:

Publisher:

ISBN: UOM:39015033852933

Category: English imprints

Page:

View: 290

Categories: English imprints