Nonconvex Optimization In Mechanics

Author : E.S. Mistakidis,Georgios E. Stavroulakis
Publisher : Springer Science & Business Media
Page : 295 pages
File Size : 40,5 Mb
Release : 2013-11-21
Category : Technology & Engineering
ISBN : 9781461558293

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Nonconvex Optimization in Mechanics by E.S. Mistakidis,Georgios E. Stavroulakis Pdf

Nonconvexity and nonsmoothness arise in a large class of engineering applica tions. In many cases of practical importance the possibilities offered by opti mization with its algorithms and heuristics can substantially improve the per formance and the range of applicability of classical computational mechanics algorithms. For a class of problems this approach is the only one that really works. The present book presents in a comprehensive way the application of opti mization algorithms and heuristics in smooth and nonsmooth mechanics. The necessity of this approach is presented to the reader through simple, represen tative examples. As things become more complex, the necessary material from convex and nonconvex optimization and from mechanics are introduced in a self-contained way. Unilateral contact and friction problems, adhesive contact and delamination problems, nonconvex elastoplasticity, fractal friction laws, frames with semi rigid connections, are among the applications which are treated in details here. Working algorithms are given for each application and are demonstrated by means of representative examples. The interested reader will find helpful references to up-to-date scientific and technical literature so that to be able to work on research or engineering topics which are not directly covered here.

Author : David Yang Gao,Raymond W. Ogden,Georgios E. Stavroulakis
Publisher : Springer Science & Business Media
Page : 505 pages
File Size : 40,8 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9781461302759

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Nonsmooth/Nonconvex Mechanics by David Yang Gao,Raymond W. Ogden,Georgios E. Stavroulakis Pdf

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.

Author : Vladimir F. Demyanov,Georgios E. Stavroulakis,L.N. Polyakova,P. D. Panagiotopoulos
Publisher : Springer Science & Business Media
Page : 362 pages
File Size : 41,5 Mb
Release : 2013-11-21
Category : Computers
ISBN : 9781461541134

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Quasidifferentiability and Nonsmooth Modelling in Mechanics, Engineering and Economics by Vladimir F. Demyanov,Georgios E. Stavroulakis,L.N. Polyakova,P. D. Panagiotopoulos Pdf

Nonsmooth energy functions govern phenomena which occur frequently in nature and in all areas of life. They constitute a fascinating subject in mathematics and permit the rational understanding of yet unsolved or partially solved questions in mechanics, engineering and economics. This is the first book to provide a complete and rigorous presentation of the quasidifferentiability approach to nonconvex, possibly nonsmooth, energy functions, of the derivation and study of the corresponding variational expressions in mechanics, engineering and economics, and of their numerical treatment. The new variational formulations derived are illustrated by many interesting numerical problems. The techniques presented will permit the reader to check any solution obtained by other heuristic techniques for nonconvex, nonsmooth energy problems. A civil, mechanical or aeronautical engineer can find in the book the only existing mathematically sound technique for the formulation and study of nonconvex, nonsmooth energy problems. Audience: The book will be of interest to pure and applied mathematicians, physicists, researchers in mechanics, civil, mechanical and aeronautical engineers, structural analysts and software developers. It is also suitable for graduate courses in nonlinear mechanics, nonsmooth analysis, applied optimization, control, calculus of variations and computational mechanics.

Author : P. Brousse
Publisher : Elsevier
Page : 292 pages
File Size : 42,7 Mb
Release : 2013-10-22
Category : Technology & Engineering
ISBN : 9781483290140

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Optimization in Mechanics by P. Brousse Pdf

Optimization in Mechanics: Problems and Methods investigates various problems and methods of optimization in mechanics. The subjects under study range from minimization of masses and stresses or displacements, to maximization of loads, vibration frequencies, and critical speeds of rotating shafts. Comprised of seven chapters, this book begins by presenting examples of optimization problems in mechanics and considering their application, as well as illustrating the usefulness of some optimizations like those of a reinforced shell, a robot, and a booster. The next chapter outlines some of the mathematical concepts that form the framework for optimization methods and techniques and demonstrates their efficiency in yielding relevant results. Subsequent chapters focus on the Kuhn Tucker theorem and duality, with proofs; associated problems and classical numerical methods of mathematical programming, including gradient and conjugate gradient methods; and techniques for dealing with large-scale problems. The book concludes by describing optimizations of discrete or continuous structures subject to dynamical effects. Mass minimization and fundamental eigenvalue problems as well as problems of minimization of some dynamical responses are studied. This monograph is written for students, engineers, scientists, and even self-taught individuals.

Author : G. Isac
Publisher : Springer Science & Business Media
Page : 691 pages
File Size : 40,9 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9781475731415

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Topological Methods in Complementarity Theory by G. Isac Pdf

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.

Author : David Yang Gao
Publisher : Springer Science & Business Media
Page : 463 pages
File Size : 47,7 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9781475731767

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Duality Principles in Nonconvex Systems by David Yang Gao Pdf

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.

Author : Roman G. Strongin,Yaroslav D. Sergeyev
Publisher : Springer Science & Business Media
Page : 742 pages
File Size : 54,7 Mb
Release : 2000-10-31
Category : Computers
ISBN : 0792364902

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Global Optimization with Non-Convex Constraints by Roman G. Strongin,Yaroslav D. Sergeyev Pdf

This book presents a new approach to global non-convex constrained optimization. Problem dimensionality is reduced via space-filling curves. To economize the search, constraint is accounted separately (penalties are not employed). The multicriteria case is also considered. All techniques are generalized for (non-redundant) execution on multiprocessor systems. Audience: Researchers and students working in optimization, applied mathematics, and computer science.

Author : R.P. Gilbert,Panagiotis D. Panagiotopoulos,Panos M. Pardalos
Publisher : Springer Science & Business Media
Page : 395 pages
File Size : 45,9 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9781461302872

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From Convexity to Nonconvexity by R.P. Gilbert,Panagiotis D. Panagiotopoulos,Panos M. Pardalos Pdf

This collection of papers is dedicated to the memory of Gaetano Fichera, a great mathematician and also a good friend to the editors. Regrettably it took an unusual amount of time to bring this collection out. This was primarily due to the fact that the main editor who had collected all of the materials, for this volume, P. D. Panagiotopoulos, died unexpectedly during the period when we were editing the manuscript. The other two editors in appreciation of Panagiotopoulos' contribution to this field, believe it is therefore fitting that this collection be dedicated to his memory also. The theme of the collection is centered around the seminal research of G. Fichera on the Signorini problem. Variants on this idea enter in different ways. For example, by bringing in friction the problem is no longer self-adjoint and the minimization formulation is not valid. A large portion of this collection is devoted to survey papers concerning hemivariational methods, with a main point of its application to nonsmooth mechanics. Hemivariational inequali ties, which are a generalization of variational inequalities, were pioneered by Panagiotopoulos. There are many applications of this theory to the study of non convex energy functionals occurring in many branches of mechanics. An area of concentration concerns contact problems, in particular, quasistatic and dynamic contact problems with friction and damage. Nonsmooth optimization methods which may be divided into the main groups of subgradient methods and bundle methods are also discussed in this collection.

Author : David Y. Gao,Hanif D. Sherali
Publisher : Springer Science & Business Media
Page : 520 pages
File Size : 51,8 Mb
Release : 2009-04-09
Category : Mathematics
ISBN : 9780387757148

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Advances in Applied Mathematics and Global Optimization by David Y. Gao,Hanif D. Sherali Pdf

The articles that comprise this distinguished annual volume for the Advances in Mechanics and Mathematics series have been written in honor of Gilbert Strang, a world renowned mathematician and exceptional person. Written by leading experts in complementarity, duality, global optimization, and quantum computations, this collection reveals the beauty of these mathematical disciplines and investigates recent developments in global optimization, nonconvex and nonsmooth analysis, nonlinear programming, theoretical and engineering mechanics, large scale computation, quantum algorithms and computation, and information theory.

Author : Anonim
Publisher : Unknown
Page : 276 pages
File Size : 46,7 Mb
Release : 1974
Category : Mechanics, Applied
ISBN : UCAL:C2682448

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Applied Mechanics Reviews by Anonim Pdf

Author : Christodoulos A. Floudas
Publisher : Springer Science & Business Media
Page : 741 pages
File Size : 53,8 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9781475749496

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Deterministic Global Optimization by Christodoulos A. Floudas Pdf

The vast majority of important applications in science, engineering and applied science are characterized by the existence of multiple minima and maxima, as well as first, second and higher order saddle points. The area of Deterministic Global Optimization introduces theoretical, algorithmic and computational ad vances that (i) address the computation and characterization of global minima and maxima, (ii) determine valid lower and upper bounds on the global minima and maxima, and (iii) address the enclosure of all solutions of nonlinear con strained systems of equations. Global optimization applications are widespread in all disciplines and they range from atomistic or molecular level to process and product level representations. The primary goal of this book is three fold : first, to introduce the reader to the basics of deterministic global optimization; second, to present important theoretical and algorithmic advances for several classes of mathematical prob lems that include biconvex and bilinear; problems, signomial problems, general twice differentiable nonlinear problems, mixed integer nonlinear problems, and the enclosure of all solutions of nonlinear constrained systems of equations; and third, to tie the theory and methods together with a variety of important applications.

Author : Peter J. Moss,Rajesh P. Dhakal
Publisher : CRC Press
Page : 1081 pages
File Size : 47,7 Mb
Release : 2020-10-28
Category : Technology & Engineering
ISBN : 9781000116175

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Progress in Mechanics of Structures and Materials by Peter J. Moss,Rajesh P. Dhakal Pdf

This is a collection of peer-reviewed papers originally presented at the 19th Australasian Conference on the Mechanics of Structures and Materials by academics, researchers and practitioners largely from Australasia and the Asia-Pacific region. The topics under discussion include: composite structures and materials; computational mechanics; dynamic analysis of structures; earthquake engineering; fire engineering; geomechanics and foundation engineering; mechanics of materials; reinforced and prestressed concrete structures; shock and impact loading; steel structures; structural health monitoring and damage identification; structural mechanics; and timber engineering. It is a valuable reference for academics, researchers, and civil and mechanical engineers working in structural and material engineering and mechanics.

Author : Shashi K. Mishra
Publisher : Springer Science & Business Media
Page : 276 pages
File Size : 44,6 Mb
Release : 2011-05-21
Category : Business & Economics
ISBN : 9781441996404

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Topics in Nonconvex Optimization by Shashi K. Mishra Pdf

Nonconvex Optimization is a multi-disciplinary research field that deals with the characterization and computation of local/global minima/maxima of nonlinear, nonconvex, nonsmooth, discrete and continuous functions. Nonconvex optimization problems are frequently encountered in modeling real world systems for a very broad range of applications including engineering, mathematical economics, management science, financial engineering, and social science. This contributed volume consists of selected contributions from the Advanced Training Programme on Nonconvex Optimization and Its Applications held at Banaras Hindu University in March 2009. It aims to bring together new concepts, theoretical developments, and applications from these researchers. Both theoretical and applied articles are contained in this volume which adds to the state of the art research in this field. Topics in Nonconvex Optimization is suitable for advanced graduate students and researchers in this area.

Author : Jonathan F. Bard
Publisher : Springer Science & Business Media
Page : 484 pages
File Size : 53,7 Mb
Release : 2013-03-09
Category : Business & Economics
ISBN : 9781475728361

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Practical Bilevel Optimization by Jonathan F. Bard Pdf

The use of optimization techniques has become integral to the design and analysis of most industrial and socio-economic systems. Great strides have been made recently in the solution of large-scale problems arising in such areas as production planning, airline scheduling, government regulation, and engineering design, to name a few. Analysts have found, however, that standard mathematical programming models are often inadequate in these situations because more than a single objective function and a single decision maker are involved. Multiple objective programming deals with the extension of optimization techniques to account for several objective functions, while game theory deals with the inter-personal dynamics surrounding conflict. Bilevel programming, the focus of this book, is in a narrow sense the combination of the two. It addresses the problern in which two decision makers, each with their individual objectives, act and react in a noncooperative, sequential manner. The actions of one affect the choices and payoffs available to the other but neither player can completely dominate the other in the traditional sense.

Author : Christodoulos A. Floudas
Publisher : Springer Science & Business Media
Page : 774 pages
File Size : 47,5 Mb
Release : 2000
Category : Computers
ISBN : 0792360141

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Deterministic Global Optimization by Christodoulos A. Floudas Pdf

This book provides a unified and insightful treatment of deterministic global optimization. It introduces theoretical and algorithmic advances that address the computation and characterization of global optima, determine valid lower and upper bounds on the global minima and maxima, and enclose all solutions of nonlinear constrained systems of equations. Among its special features, the book: Introduces the fundamentals of deterministic global optimization; Provides a thorough treatment of decomposition-based global optimization approaches for biconvex and bilinear problems; Covers global optimization methods for generalized geometric programming problems Presents in-depth global optimization algorithms for general twice continuously differentiable nonlinear problems; Provides a detailed treatment of global optimization methods for mixed-integer nonlinear problems; Develops global optimization approaches for the enclosure of all solutions of nonlinear constrained systems of equations; Includes many important applications from process design, synthesis, control, and operations, phase equilibrium, design under uncertainty, parameter estimation, azeotrope prediction, structure prediction in clusters and molecules, protein folding, and peptide docking. Audience: This book can be used as a textbook in graduate-level courses and as a desk reference for researchers in all branches of engineering and applied science, applied mathematics, industrial engineering, operations research, computer science, economics, computational chemistry and molecular biology.