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Relaxation In Optimization Theory And Variational Calculus
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Book Synopsis Relaxation in Optimization Theory and Variational Calculus by : Tomáš Roubiček
Download or read book Relaxation in Optimization Theory and Variational Calculus written by Tomáš Roubiček and published by Walter de Gruyter. This book was released on 1997 with total page 496 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduces applied mathematicians and graduate students to an original relaxation method based on a continuous extension of various optimization problems relating to convex compactification; it can be applied to problems in optimal control theory, the calculus of variations, and non-cooperative game theory. Reviews the background and summarizes the general theory of convex compactifications, then uses it to obtain convex, locally compact envelopes of the Lebesague and Sobolev spaces involved in concrete problems. The nontrivial envelopes cover the classical Young measures as well as various generalizations of them, which can record the limit behavior of fast oscillation and concentration effects. Annotation copyrighted by Book News, Inc., Portland, OR
Book Synopsis Relaxation in Optimization Theory and Variational Calculus by : Tomáš Roubíček
Download or read book Relaxation in Optimization Theory and Variational Calculus written by Tomáš Roubíček and published by Walter de Gruyter GmbH & Co KG. This book was released on 2020-11-09 with total page 602 pages. Available in PDF, EPUB and Kindle. Book excerpt: The relaxation method has enjoyed an intensive development during many decades and this new edition of this comprehensive text reflects in particular the main achievements in the past 20 years. Moreover, many further improvements and extensions are included, both in the direction of optimal control and optimal design as well as in numerics and applications in materials science, along with an updated treatment of the abstract parts of the theory.
Book Synopsis Calculus of Variations and Optimal Control by : Alexander Ioffe
Download or read book Calculus of Variations and Optimal Control written by Alexander Ioffe and published by CRC Press. This book was released on 2021-02-27 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: The calculus of variations is a classical area of mathematical analysis-300 years old-yet its myriad applications in science and technology continue to hold great interest and keep it an active area of research. These two volumes contain the referenced proceedings of the international conference on Calculus of Variations and Related Topics held at the Technion-Israel Institute of Technology in March 1998. The conference commemorated 300 years of work in the field and brought together many of its leading experts. The papers in the first volume focus on critical point theory and differential equations. The other volume deals with variational aspects of optimal control. Together they provide a unique opportunity to review the state-of-the-art of the calculus of variations, as presented by an international panel of masters in the field.
Book Synopsis Theory and Numerics of Differential Equations by : James Blowey
Download or read book Theory and Numerics of Differential Equations written by James Blowey and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: A compilation of detailed lecture notes on six topics at the forefront of current research in numerical analysis and applied mathematics. Each set of notes presents a self-contained guide to a current research area and has an extensive bibliography. In addition, most of the notes contain detailed proofs of the key results. The notes start from a level suitable for first year graduate students in applied mathematics, mathematical analysis or numerical analysis, and proceed to current research topics. The reader should therefore be able to quickly gain an insight into the important results and techniques in each area without recourse to the large research literature. Current (unsolved) problems are also described and directions for future research is given.
Book Synopsis Robust Optimization-Directed Design by : Andrew J. Kurdila
Download or read book Robust Optimization-Directed Design written by Andrew J. Kurdila and published by Springer Science & Business Media. This book was released on 2006-06-04 with total page 279 pages. Available in PDF, EPUB and Kindle. Book excerpt: Robust design—that is, managing design uncertainties such as model uncertainty or parametric uncertainty—is the often unpleasant issue crucial in much multidisciplinary optimal design work. Recently, there has been enormous practical interest in strategies for applying optimization tools to the development of robust solutions and designs in several areas, including aerodynamics, the integration of sensing (e.g., laser radars, vision-based systems, and millimeter-wave radars) and control, cooperative control with poorly modeled uncertainty, cascading failures in military and civilian applications, multi-mode seekers/sensor fusion, and data association problems and tracking systems. The contributions to this book explore these different strategies. The expression "optimization-directed” in this book’s title is meant to suggest that the focus is not agonizing over whether optimization strategies identify a true global optimum, but rather whether these strategies make significant design improvements.
Book Synopsis Young Measures and Compactness in Measure Spaces by : Liviu C. Florescu
Download or read book Young Measures and Compactness in Measure Spaces written by Liviu C. Florescu and published by Walter de Gruyter. This book was released on 2012-05-29 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years, technological progress created a great need for complex mathematical models. Many practical problems can be formulated using optimization theory and they hope to obtain an optimal solution. In most cases, such optimal solution can not be found. So, non-convex optimization problems (arising, e.g., in variational calculus, optimal control, nonlinear evolutions equations) may not possess a classical minimizer because the minimizing sequences have typically rapid oscillations. This behavior requires a relaxation of notion of solution for such problems; often we can obtain such a relaxation by means of Young measures. This monograph is a self-contained book which gathers all theoretical aspects related to the defining of Young measures (measurability, disintegration, stable convergence, compactness), a book which is also a useful tool for those interested in theoretical foundations of the measure theory. It provides a complete set of classical and recent compactness results in measure and function spaces. The book is organized in three chapters: The first chapter covers background material on measure theory in abstract frame. In the second chapter the measure theory on topological spaces is presented. Compactness results from the first two chapters are used to study Young measures in the third chapter. All results are accompanied by full demonstrations and for many of these results different proofs are given. All statements are fully justified and proved.
Book Synopsis Fast Solution of Discretized Optimization Problems by : Karl-Heinz Hoffmann
Download or read book Fast Solution of Discretized Optimization Problems written by Karl-Heinz Hoffmann and published by Birkhäuser. This book was released on 2012-12-06 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: A collection of articles summarizing the state of knowledge in a large portion of modern homotopy theory. This welcome reference for many new results and recent methods is addressed to all mathematicians interested in homotopy theory and in geometric aspects of group theory.
Book Synopsis Mathematical Methods in Scattering Theory and Biomedical Engineering by : Dimitrios Ioannou Fotiadis
Download or read book Mathematical Methods in Scattering Theory and Biomedical Engineering written by Dimitrios Ioannou Fotiadis and published by World Scientific. This book was released on 2006 with total page 454 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume comprises the papers presented at the Seventh International Workshop on Scattering Theory and Biomedical Engineering, focusing on the hottest topics in scattering theory and biomedical technology.All the contributions are state-of-the-art and have been fully reviewed. The authors are recognized as being eminent both in their field and in the science community.
Book Synopsis Mathematical Methods In Scattering Theory And Biomedical Engineering - Proceedings Of The Seventh International Workshop by : Christos V Massalas
Download or read book Mathematical Methods In Scattering Theory And Biomedical Engineering - Proceedings Of The Seventh International Workshop written by Christos V Massalas and published by World Scientific. This book was released on 2006-08-01 with total page 454 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume comprises the papers presented at the Seventh International Workshop on Scattering Theory and Biomedical Engineering, focusing on the hottest topics in scattering theory and biomedical technology.All the contributions are state-of-the-art and have been fully reviewed. The authors are recognized as being eminent both in their field and in the science community.
Book Synopsis Analysis and Simulation of Multifield Problems by : Wolfgang L. Wendland
Download or read book Analysis and Simulation of Multifield Problems written by Wolfgang L. Wendland and published by Springer Science & Business Media. This book was released on 2012-11-10 with total page 389 pages. Available in PDF, EPUB and Kindle. Book excerpt: The analysis and simulation of multifield problems have recently become one of the most actual and vivid areas of research. Although the individual subproblems of complex technical and physical phenomena often are understood separately, their interaction and coupling create not only new difficulties but also a complete new level and quality of interacting coupled field problems. Presented by leading experts this book includes recent results in these fields from the International Conference on Multifield Problems, April 8-10, 2002 at the University of Stuttgart, Germany.
Book Synopsis Analysis, Modeling and Simulation of Multiscale Problems by : Alexander Mielke
Download or read book Analysis, Modeling and Simulation of Multiscale Problems written by Alexander Mielke and published by Springer Science & Business Media. This book was released on 2006-10-14 with total page 704 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book reports recent mathematical developments in the Programme "Analysis, Modeling and Simulation of Multiscale Problems", which started as a German research initiative in 2006. Multiscale problems occur in many fields of science, such as microstructures in materials, sharp-interface models, many-particle systems and motions on different spatial and temporal scales in quantum mechanics or in molecular dynamics. The book presents current mathematical foundations of modeling, and proposes efficient numerical treatment.
Book Synopsis IUTAM Symposium on Computational Mechanics of Solid Materials at Large Strains by : Christian Miehe
Download or read book IUTAM Symposium on Computational Mechanics of Solid Materials at Large Strains written by Christian Miehe and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 487 pages. Available in PDF, EPUB and Kindle. Book excerpt: The steady increase in computational power induces an equally steady increase in the complexity of the engineering models and associated computer codes. This particularly affects the modeling of the mechanical response of materials. Material behavior is nowadays modeled in the strongly nonlinear range by tak ing into account finite strains, complex hysteresis effects, fracture phenomena and multiscale features. Progress in this field is of fundamental importance for many engineering disciplines, especially those concerned with material testing, safety, reliability and serviceability analyses of engineering structures. In recent years many important achievements have been made in the field of the theoretical formulation, the mathematical analysis and the numerical im plementation of deformation processes in solids. Computational methods and simulation techniques today play a central role in advancing the understanding of complex material behavior. Research in the field of "ComputationalMechan ics of Materials" is concerned with the development of mathematical models and numerical solution techniques for the simulation of material response. It is a very broad interdisciplinary field of science with inputs from traditional fields such as Applied Mechanics, Applied Mathematics, Materials Science, Solid State Physics and Information Technology. The intention of the IUTAM Symposium "Computational Mechanics of Solid Materials at Large Strains", held at the University of Stuttgart, Germany, from August 20-24, 200I, was to give a state of the art and a survey about recent developments in this field and to create perspectives for future research trends.
Book Synopsis Large-Scale Scientific Computing by : Ivan Lirkov
Download or read book Large-Scale Scientific Computing written by Ivan Lirkov and published by Springer Science & Business Media. This book was released on 2004-02-18 with total page 493 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the thoroughly refereed post-proceedings of the 4th International Conference on Large-Scale Scientific Computations, LSSC 2003, held in Sozopol, Bulgaria in June 2003. The 50 revised full papers presented together with 5 invited papers were carefully reviewed and selected for inclusion in the book. The papers are organized in topical sections on preconditioning techniques, Monte Carlo methods and quasi-Monte-Carlo methods, set-value of numerics and reliable computing, environmental modeling, and large-scale computations for engineering problems.
Book Synopsis Numerical Methods and Applications by : Ivan Dimov
Download or read book Numerical Methods and Applications written by Ivan Dimov and published by Springer. This book was released on 2003-07-01 with total page 570 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the thoroughly refereed post-proceedings of the 5th International Conference on Numerical Methods and Applications, NMA 2002, held in Borovets, Bulgaria, in August 2002. The 58 revised full papers presented together with 6 invited papers were carefully selected from numerous submissions during two rounds of reviewing and improvement. In accordance with various mini-symposia, the papers are organized in topical sections on Monte Carlo and Quasi-Monte Carlo methods, robust iterative solution methods and applications, control and uncertainty systems, numerical methods for sensor data processing, as well as in a section comprising various other methods, tools, and applications.
Book Synopsis A Relaxation-Based Approach to Optimal Control of Hybrid and Switched Systems by : Vadim Azhmyakov
Download or read book A Relaxation-Based Approach to Optimal Control of Hybrid and Switched Systems written by Vadim Azhmyakov and published by Butterworth-Heinemann. This book was released on 2019-02-14 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Relaxation Based Approach to Optimal Control of Hybrid and Switched Systems proposes a unified approach to effective and numerically tractable relaxation schemes for optimal control problems of hybrid and switched systems. The book gives an overview of the existing (conventional and newly developed) relaxation techniques associated with the conventional systems described by ordinary differential equations. Next, it constructs a self-contained relaxation theory for optimal control processes governed by various types (sub-classes) of general hybrid and switched systems. It contains all mathematical tools necessary for an adequate understanding and using of the sophisticated relaxation techniques. In addition, readers will find many practically oriented optimal control problems related to the new class of dynamic systems. All in all, the book follows engineering and numerical concepts. However, it can also be considered as a mathematical compendium that contains the necessary formal results and important algorithms related to the modern relaxation theory. - Illustrates the use of the relaxation approaches in engineering optimization - Presents application of the relaxation methods in computational schemes for a numerical treatment of the sophisticated hybrid/switched optimal control problems - Offers a rigorous and self-contained mathematical tool for an adequate understanding and practical use of the relaxation techniques - Presents an extension of the relaxation methodology to the new class of applied dynamic systems, namely, to hybrid and switched control systems
Book Synopsis Modelling and Optimization of Distributed Parameter Systems Applications to engineering by : K. Malanowski
Download or read book Modelling and Optimization of Distributed Parameter Systems Applications to engineering written by K. Malanowski and published by Springer. This book was released on 2013-06-05 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Numerical Analysis and Its Applications by : Zhilin Li
Download or read book Numerical Analysis and Its Applications written by Zhilin Li and published by Springer Science & Business Media. This book was released on 2005-02-21 with total page 642 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the thoroughly refereed post-proceedings of the Third International Conference on Numerical Analysis and Its Applications, NAA 2004, held in Rousse, Bulgaria in June/July 2004. The 68 revised full papers presented together with 8 invited papers were carefully selected during two rounds of reviewing and improvement. All current aspects of numerical analysis are addressed. Among the application fields covered are computational sciences and engineering, chemistry, physics, economics, simulation, fluid dynamics, visualization, etc.
