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Book Control and Optimization with PDE Constraints

Download or read book Control and Optimization with PDE Constraints written by Kristian Bredies and published by Springer Science & Business Media. This book was released on 2013-06-12 with total page 221 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many mathematical models of physical, biological and social systems involve partial differential equations (PDEs). The desire to understand and influence these systems naturally leads to considering problems of control and optimization. This book presents important topics in the areas of control of PDEs and of PDE-constrained optimization, covering the full spectrum from analysis to numerical realization and applications. Leading scientists address current topics such as non-smooth optimization, Hamilton–Jacobi–Bellmann equations, issues in optimization and control of stochastic partial differential equations, reduced-order models and domain decomposition, discretization error estimates for optimal control problems, and control of quantum-dynamical systems. These contributions originate from the “International Workshop on Control and Optimization of PDEs” in Mariatrost in October 2011. This book is an excellent resource for students and researchers in control or optimization of differential equations. Readers interested in theory or in numerical algorithms will find this book equally useful.

Book Trends in PDE Constrained Optimization

Download or read book Trends in PDE Constrained Optimization written by Günter Leugering and published by Springer. This book was released on 2014-12-22 with total page 539 pages. Available in PDF, EPUB and Kindle. Book excerpt: Optimization problems subject to constraints governed by partial differential equations (PDEs) are among the most challenging problems in the context of industrial, economical and medical applications. Almost the entire range of problems in this field of research was studied and further explored as part of the Deutsche Forschungsgemeinschaft (DFG) priority program 1253 on “Optimization with Partial Differential Equations” from 2006 to 2013. The investigations were motivated by the fascinating potential applications and challenging mathematical problems that arise in the field of PDE constrained optimization. New analytic and algorithmic paradigms have been developed, implemented and validated in the context of real-world applications. In this special volume, contributions from more than fifteen German universities combine the results of this interdisciplinary program with a focus on applied mathematics. The book is divided into five sections on “Constrained Optimization, Identification and Control”, “Shape and Topology Optimization”, “Adaptivity and Model Reduction”, “Discretization: Concepts and Analysis” and “Applications”. Peer-reviewed research articles present the most recent results in the field of PDE constrained optimization and control problems. Informative survey articles give an overview of topics that set sustainable trends for future research. This makes this special volume interesting not only for mathematicians, but also for engineers and for natural and medical scientists working on processes that can be modeled by PDEs.

Book Issues in Robotics and Automation 2013 Edition

Download or read book Issues in Robotics and Automation 2013 Edition written by and published by ScholarlyEditions. This book was released on 2013-05-01 with total page 1196 pages. Available in PDF, EPUB and Kindle. Book excerpt: Issues in Robotics and Automation / 2013 Edition is a ScholarlyEditions™ book that delivers timely, authoritative, and comprehensive information about Computing Information and Control. The editors have built Issues in Robotics and Automation: 2013 Edition on the vast information databases of ScholarlyNews.™ You can expect the information about Computing Information and Control in this book to be deeper than what you can access anywhere else, as well as consistently reliable, authoritative, informed, and relevant. The content of Issues in Robotics and Automation: 2013 Edition has been produced by the world’s leading scientists, engineers, analysts, research institutions, and companies. All of the content is from peer-reviewed sources, and all of it is written, assembled, and edited by the editors at ScholarlyEditions™ and available exclusively from us. You now have a source you can cite with authority, confidence, and credibility. More information is available at http://www.ScholarlyEditions.com/.

Book Elliptic Problems in Nonsmooth Domains

Download or read book Elliptic Problems in Nonsmooth Domains written by Pierre Grisvard and published by SIAM. This book was released on 1985-01-01 with total page 430 pages. Available in PDF, EPUB and Kindle. Book excerpt: This classic text focuses on elliptic boundary value problems in domains with nonsmooth boundaries and on problems with mixed boundary conditions. Its contents are essential for an understanding of the behavior of numerical methods for partial differential equations (PDEs) on two-dimensional domains with corners. Elliptic problems in nonsmooth domains: provides a careful and self-contained development of Sobolev spaces on nonsmooth domains, develops a comprehensive theory for second-order elliptic boundary value problems, and addresses fourth-order boundary value problems and numerical treatment of singularities.

Book Optimization of Elliptic Systems

Download or read book Optimization of Elliptic Systems written by Pekka Neittaanmaki and published by Springer Science & Business Media. This book was released on 2007-01-04 with total page 514 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present monograph is intended to provide a comprehensive and accessible introduction to the optimization of elliptic systems. This area of mathematical research, which has many important applications in science and technology. has experienced an impressive development during the past two decades. There are already many good textbooks dealing with various aspects of optimal design problems. In this regard, we refer to the works of Pironneau [1984], Haslinger and Neittaanmaki [1988], [1996], Sokolowski and Zolksio [1992], Litvinov [2000], Allaire [2001], Mohammadi and Pironneau [2001], Delfour and Zolksio [2001], and Makinen and Haslinger [2003]. Already Lions [I9681 devoted a major part of his classical monograph on the optimal control of partial differential equations to the optimization of elliptic systems. Let us also mention that even the very first known problem of the calculus of variations, the brachistochrone studied by Bernoulli back in 1696. is in fact a shape optimization problem. The natural richness of this mathematical research subject, as well as the extremely large field of possible applications, has created the unusual situation that although many important results and methods have already been est- lished, there are still pressing unsolved questions. In this monograph, we aim to address some of these open problems; as a consequence, there is only a minor overlap with the textbooks already existing in the field.

Book Elliptic Equations in Polyhedral Domains

Download or read book Elliptic Equations in Polyhedral Domains written by V. G. Maz_i_a and published by American Mathematical Soc.. This book was released on 2010-04-22 with total page 618 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first monograph which systematically treats elliptic boundary value problems in domains of polyhedral type. The authors mainly describe their own recent results focusing on the Dirichlet problem for linear strongly elliptic systems of arbitrary order, Neumann and mixed boundary value problems for second order systems, and on boundary value problems for the stationary Stokes and Navier-Stokes systems. A feature of the book is the systematic use of Green's matrices. Using estimates for the elements of these matrices, the authors obtain solvability and regularity theorems for the solutions in weighted and non-weighted Sobolev and Holder spaces. Some classical problems of mathematical physics (Laplace and biharmonic equations, Lame system) are considered as examples. Furthermore, the book contains maximum modulus estimates for the solutions and their derivatives. The exposition is self-contained, and an introductory chapter provides background material on the theory of elliptic boundary value problems in domains with smooth boundaries and in domains with conical points. The book is destined for graduate students and researchers working in elliptic partial differential equations and applications.

Book Maximum Principle for State constrained Optimal Control Problems Governed by Quasilinear Elliptic Equations

Download or read book Maximum Principle for State constrained Optimal Control Problems Governed by Quasilinear Elliptic Equations written by University of Minnesota. Institute for Mathematics and Its Applications and published by . This book was released on 1992 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Book A Gradient Computational Technique for a Class of Optimal Control Problems Subject to Inequality Constraints

Download or read book A Gradient Computational Technique for a Class of Optimal Control Problems Subject to Inequality Constraints written by Shyh Jong Wang and published by . This book was released on 1969 with total page 334 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Book Lagrange Multiplier Approach to Variational Problems and Applications

Download or read book Lagrange Multiplier Approach to Variational Problems and Applications written by Kazufumi Ito and published by SIAM. This book was released on 2008-11-06 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: Analyses Lagrange multiplier theory and demonstrates its impact on the development of numerical algorithms for variational problems in function spaces.

Book An Extension of Pontryagin s Principle for State constrained Optimal Control of Semilinear Elliptic Equations and Variational Inequalities

Download or read book An Extension of Pontryagin s Principle for State constrained Optimal Control of Semilinear Elliptic Equations and Variational Inequalities written by Institut National de Recherche en Informatique et en Automatique and published by . This book was released on 1992 with total page 28 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Book The Minimization of an L 462 functional Subject to an Elliptic PDE and State Constraints

Download or read book The Minimization of an L 462 functional Subject to an Elliptic PDE and State Constraints written by Uwe Prüfert and published by . This book was released on 2008 with total page 29 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: "We study the optimal control of a maximum-norm objective functional subjected to an elliptic-type PDE and pointwise state constraints. The problem is transformed into a problem where the non-differentiable L[superscript infinity]-norm in the functional will be replaced by a scalar variable and additional state constraints. This problem is solved by barrier methods. We will show the existence and convergence of the central path for a class of barrier functions. Numerical experiments complete the presentation."