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Optimal Control Of Partial Differential Equations Involving Pointwise State Constraints Regularization And Applications
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Book Synopsis Optimal Control of Partial Differential Equations Involving Pointwise State Constraints: Regularization and Applications by : Irwin Yousept
Download or read book Optimal Control of Partial Differential Equations Involving Pointwise State Constraints: Regularization and Applications written by Irwin Yousept and published by Cuvillier Verlag. This book was released on 2008 with total page 26 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Constrained Optimization and Optimal Control for Partial Differential Equations by : Günter Leugering
Download or read book Constrained Optimization and Optimal Control for Partial Differential Equations written by Günter Leugering and published by Birkhäuser. This book was released on 2014-02-23 with total page 624 pages. Available in PDF, EPUB and Kindle. Book excerpt: This special volume focuses on optimization and control of processes governed by partial differential equations. The contributors are mostly participants of the DFG-priority program 1253: Optimization with PDE-constraints which is active since 2006. The book is organized in sections which cover almost the entire spectrum of modern research in this emerging field. Indeed, even though the field of optimal control and optimization for PDE-constrained problems has undergone a dramatic increase of interest during the last four decades, a full theory for nonlinear problems is still lacking. The contributions of this volume, some of which have the character of survey articles, therefore, aim at creating and developing further new ideas for optimization, control and corresponding numerical simulations of systems of possibly coupled nonlinear partial differential equations. The research conducted within this unique network of groups in more than fifteen German universities focuses on novel methods of optimization, control and identification for problems in infinite-dimensional spaces, shape and topology problems, model reduction and adaptivity, discretization concepts and important applications. Besides the theoretical interest, the most prominent question is about the effectiveness of model-based numerical optimization methods for PDEs versus a black-box approach that uses existing codes, often heuristic-based, for optimization.
Book Synopsis Optimal Control of Partial Differential Equations by : Andrea Manzoni
Download or read book Optimal Control of Partial Differential Equations written by Andrea Manzoni and published by Springer Nature. This book was released on 2022-01-01 with total page 507 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a book on optimal control problems (OCPs) for partial differential equations (PDEs) that evolved from a series of courses taught by the authors in the last few years at Politecnico di Milano, both at the undergraduate and graduate levels. The book covers the whole range spanning from the setup and the rigorous theoretical analysis of OCPs, the derivation of the system of optimality conditions, the proposition of suitable numerical methods, their formulation, their analysis, including their application to a broad set of problems of practical relevance. The first introductory chapter addresses a handful of representative OCPs and presents an overview of the associated mathematical issues. The rest of the book is organized into three parts: part I provides preliminary concepts of OCPs for algebraic and dynamical systems; part II addresses OCPs involving linear PDEs (mostly elliptic and parabolic type) and quadratic cost functions; part III deals with more general classes of OCPs that stand behind the advanced applications mentioned above. Starting from simple problems that allow a “hands-on” treatment, the reader is progressively led to a general framework suitable to face a broader class of problems. Moreover, the inclusion of many pseudocodes allows the reader to easily implement the algorithms illustrated throughout the text. The three parts of the book are suitable to readers with variable mathematical backgrounds, from advanced undergraduate to Ph.D. levels and beyond. We believe that applied mathematicians, computational scientists, and engineers may find this book useful for a constructive approach toward the solution of OCPs in the context of complex applications.
Book Synopsis Constrained Optimization and Optimal Control for Partial Differential Equations by : Günter Leugering
Download or read book Constrained Optimization and Optimal Control for Partial Differential Equations written by Günter Leugering and published by Springer Science & Business Media. This book was released on 2012-01-03 with total page 621 pages. Available in PDF, EPUB and Kindle. Book excerpt: This special volume focuses on optimization and control of processes governed by partial differential equations. The contributors are mostly participants of the DFG-priority program 1253: Optimization with PDE-constraints which is active since 2006. The book is organized in sections which cover almost the entire spectrum of modern research in this emerging field. Indeed, even though the field of optimal control and optimization for PDE-constrained problems has undergone a dramatic increase of interest during the last four decades, a full theory for nonlinear problems is still lacking. The contributions of this volume, some of which have the character of survey articles, therefore, aim at creating and developing further new ideas for optimization, control and corresponding numerical simulations of systems of possibly coupled nonlinear partial differential equations. The research conducted within this unique network of groups in more than fifteen German universities focuses on novel methods of optimization, control and identification for problems in infinite-dimensional spaces, shape and topology problems, model reduction and adaptivity, discretization concepts and important applications. Besides the theoretical interest, the most prominent question is about the effectiveness of model-based numerical optimization methods for PDEs versus a black-box approach that uses existing codes, often heuristic-based, for optimization.
Book Synopsis Optimal Control of Partial Differential Equations by : Fredi Tröltzsch
Download or read book Optimal Control of Partial Differential Equations written by Fredi Tröltzsch and published by American Mathematical Society. This book was released on 2024-03-21 with total page 417 pages. Available in PDF, EPUB and Kindle. Book excerpt: Optimal control theory is concerned with finding control functions that minimize cost functions for systems described by differential equations. The methods have found widespread applications in aeronautics, mechanical engineering, the life sciences, and many other disciplines. This book focuses on optimal control problems where the state equation is an elliptic or parabolic partial differential equation. Included are topics such as the existence of optimal solutions, necessary optimality conditions and adjoint equations, second-order sufficient conditions, and main principles of selected numerical techniques. It also contains a survey on the Karush-Kuhn-Tucker theory of nonlinear programming in Banach spaces. The exposition begins with control problems with linear equations, quadratic cost functions and control constraints. To make the book self-contained, basic facts on weak solutions of elliptic and parabolic equations are introduced. Principles of functional analysis are introduced and explained as they are needed. Many simple examples illustrate the theory and its hidden difficulties. This start to the book makes it fairly self-contained and suitable for advanced undergraduates or beginning graduate students. Advanced control problems for nonlinear partial differential equations are also discussed. As prerequisites, results on boundedness and continuity of solutions to semilinear elliptic and parabolic equations are addressed. These topics are not yet readily available in books on PDEs, making the exposition also interesting for researchers. Alongside the main theme of the analysis of problems of optimal control, Tröltzsch also discusses numerical techniques. The exposition is confined to brief introductions into the basic ideas in order to give the reader an impression of how the theory can be realized numerically. After reading this book, the reader will be familiar with the main principles of the numerical analysis of PDE-constrained optimization.
Book Synopsis Variational Analysis and Set Optimization by : Akhtar A. Khan
Download or read book Variational Analysis and Set Optimization written by Akhtar A. Khan and published by CRC Press. This book was released on 2019-06-07 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains the latest advances in variational analysis and set / vector optimization, including uncertain optimization, optimal control and bilevel optimization. Recent developments concerning scalarization techniques, necessary and sufficient optimality conditions and duality statements are given. New numerical methods for efficiently solving set optimization problems are provided. Moreover, applications in economics, finance and risk theory are discussed. Summary The objective of this book is to present advances in different areas of variational analysis and set optimization, especially uncertain optimization, optimal control and bilevel optimization. Uncertain optimization problems will be approached from both a stochastic as well as a robust point of view. This leads to different interpretations of the solutions, which widens the choices for a decision-maker given his preferences. Recent developments regarding linear and nonlinear scalarization techniques with solid and nonsolid ordering cones for solving set optimization problems are discussed in this book. These results are useful for deriving optimality conditions for set and vector optimization problems. Consequently, necessary and sufficient optimality conditions are presented within this book, both in terms of scalarization as well as generalized derivatives. Moreover, an overview of existing duality statements and new duality assertions is given. The book also addresses the field of variable domination structures in vector and set optimization. Including variable ordering cones is especially important in applications such as medical image registration with uncertainties. This book covers a wide range of applications of set optimization. These range from finance, investment, insurance, control theory, economics to risk theory. As uncertain multi-objective optimization, especially robust approaches, lead to set optimization, one main focus of this book is uncertain optimization. Important recent developments concerning numerical methods for solving set optimization problems sufficiently fast are main features of this book. These are illustrated by various examples as well as easy-to-follow-steps in order to facilitate the decision process for users. Simple techniques aimed at practitioners working in the fields of mathematical programming, finance and portfolio selection are presented. These will help in the decision-making process, as well as give an overview of nondominated solutions to choose from.
Book Synopsis Optimal Control Theory with Applications in Economics by : Thomas A. Weber
Download or read book Optimal Control Theory with Applications in Economics written by Thomas A. Weber and published by MIT Press. This book was released on 2011-09-30 with total page 387 pages. Available in PDF, EPUB and Kindle. Book excerpt: A rigorous introduction to optimal control theory, with an emphasis on applications in economics. This book bridges optimal control theory and economics, discussing ordinary differential equations, optimal control, game theory, and mechanism design in one volume. Technically rigorous and largely self-contained, it provides an introduction to the use of optimal control theory for deterministic continuous-time systems in economics. The theory of ordinary differential equations (ODEs) is the backbone of the theory developed in the book, and chapter 2 offers a detailed review of basic concepts in the theory of ODEs, including the solution of systems of linear ODEs, state-space analysis, potential functions, and stability analysis. Following this, the book covers the main results of optimal control theory, in particular necessary and sufficient optimality conditions; game theory, with an emphasis on differential games; and the application of control-theoretic concepts to the design of economic mechanisms. Appendixes provide a mathematical review and full solutions to all end-of-chapter problems. The material is presented at three levels: single-person decision making; games, in which a group of decision makers interact strategically; and mechanism design, which is concerned with a designer's creation of an environment in which players interact to maximize the designer's objective. The book focuses on applications; the problems are an integral part of the text. It is intended for use as a textbook or reference for graduate students, teachers, and researchers interested in applications of control theory beyond its classical use in economic growth. The book will also appeal to readers interested in a modeling approach to certain practical problems involving dynamic continuous-time models.
Book Synopsis Computational Mathematics, Numerical Analysis and Applications by : Mariano Mateos
Download or read book Computational Mathematics, Numerical Analysis and Applications written by Mariano Mateos and published by Springer. This book was released on 2017-08-03 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first part of this volume gathers the lecture notes of the courses of the “XVII Escuela Hispano-Francesa”, held in Gijón, Spain, in June 2016. Each chapter is devoted to an advanced topic and presents state-of-the-art research in a didactic and self-contained way. Young researchers will find a complete guide to beginning advanced work in fields such as High Performance Computing, Numerical Linear Algebra, Optimal Control of Partial Differential Equations and Quantum Mechanics Simulation, while experts in these areas will find a comprehensive reference guide, including some previously unpublished results, and teachers may find these chapters useful as textbooks in graduate courses. The second part features the extended abstracts of selected research work presented by the students during the School. It highlights new results and applications in Computational Algebra, Fluid Mechanics, Chemical Kinetics and Biomedicine, among others, offering interested researchers a convenient reference guide to these latest advances.
Book Synopsis Convexity and Optimization in Banach Spaces by : Viorel Barbu
Download or read book Convexity and Optimization in Banach Spaces written by Viorel Barbu and published by Springer Science & Business Media. This book was released on 2012-01-03 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: An updated and revised edition of the 1986 title Convexity and Optimization in Banach Spaces, this book provides a self-contained presentation of basic results of the theory of convex sets and functions in infinite-dimensional spaces. The main emphasis is on applications to convex optimization and convex optimal control problems in Banach spaces. A distinctive feature is a strong emphasis on the connection between theory and application. This edition has been updated to include new results pertaining to advanced concepts of subdifferential for convex functions and new duality results in convex programming. The last chapter, concerned with convex control problems, has been rewritten and completed with new research concerning boundary control systems, the dynamic programming equations in optimal control theory and periodic optimal control problems. Finally, the structure of the book has been modified to highlight the most recent progression in the field including fundamental results on the theory of infinite-dimensional convex analysis and includes helpful bibliographical notes at the end of each chapter.
Book Synopsis Lagrange Multiplier Approach to Variational Problems and Applications by : Kazufumi Ito
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 Synopsis Regularization Methods for Ill-Posed Optimal Control Problems by : Frank Pörner
Download or read book Regularization Methods for Ill-Posed Optimal Control Problems written by Frank Pörner and published by BoD – Books on Demand. This book was released on 2018-10-04 with total page 181 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ill-posed optimization problems appear in a wide range of mathematical applications, and their numerical solution requires the use of appropriate regularization techniques. In order to understand these techniques, a thorough analysis is inevitable. The main subject of this book are quadratic optimal control problems subject to elliptic linear or semi-linear partial differential equations. Depending on the structure of the differential equation, different regularization techniques are employed, and their analysis leads to novel results such as rate of convergence estimates.
Book Synopsis Dynamics and Control of Trajectory Tubes by : Alexander B. Kurzhanski
Download or read book Dynamics and Control of Trajectory Tubes written by Alexander B. Kurzhanski and published by Springer. This book was released on 2014-10-27 with total page 457 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph presents theoretical methods involving the Hamilton–Jacobi–Bellman formalism in conjunction with set-valued techniques of nonlinear analysis to solve significant problems in dynamics and control. The emphasis is on issues of reachability, feedback control synthesis under complex state constraints, hard or double bounds on controls, and performance in finite time. Guaranteed state estimation, output feedback control, and hybrid dynamics are also discussed. Although the focus is on systems with linear structure, the authors indicate how to apply each approach to nonlinear and nonconvex systems. The main theoretical results lead to computational schemes based on extensions of ellipsoidal calculus that provide complete solutions to the problems. These computational schemes in turn yield software tools that can be applied effectively to high-dimensional systems. Ellipsoidal Techniques for Problems of Dynamics and Control: Theory and Computation will interest graduate and senior undergraduate students, as well as researchers and practitioners interested in control theory, its applications, and its computational realizations.
Book Synopsis Non-Smooth and Complementarity-Based Distributed Parameter Systems by : Michael Hintermüller
Download or read book Non-Smooth and Complementarity-Based Distributed Parameter Systems written by Michael Hintermüller and published by Springer Nature. This book was released on 2022-02-18 with total page 518 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Optimization with PDE Constraints by : Michael Hinze
Download or read book Optimization with PDE Constraints written by Michael Hinze and published by Springer Science & Business Media. This book was released on 2008-10-16 with total page 279 pages. Available in PDF, EPUB and Kindle. Book excerpt: Solving optimization problems subject to constraints given in terms of partial d- ferential equations (PDEs) with additional constraints on the controls and/or states is one of the most challenging problems in the context of industrial, medical and economical applications, where the transition from model-based numerical si- lations to model-based design and optimal control is crucial. For the treatment of such optimization problems the interaction of optimization techniques and num- ical simulation plays a central role. After proper discretization, the number of op- 3 10 timization variables varies between 10 and 10 . It is only very recently that the enormous advances in computing power have made it possible to attack problems of this size. However, in order to accomplish this task it is crucial to utilize and f- ther explore the speci?c mathematical structure of optimization problems with PDE constraints, and to develop new mathematical approaches concerning mathematical analysis, structure exploiting algorithms, and discretization, with a special focus on prototype applications. The present book provides a modern introduction to the rapidly developing ma- ematical ?eld of optimization with PDE constraints. The ?rst chapter introduces to the analytical background and optimality theory for optimization problems with PDEs. Optimization problems with PDE-constraints are posed in in?nite dim- sional spaces. Therefore, functional analytic techniques, function space theory, as well as existence- and uniqueness results for the underlying PDE are essential to study the existence of optimal solutions and to derive optimality conditions.
Author :R. Tyrrell Rockafellar Publisher :Springer Science & Business Media ISBN 13 :3642024319 Total Pages :747 pages Book Rating :4.6/5 (42 download)
Book Synopsis Variational Analysis by : R. Tyrrell Rockafellar
Download or read book Variational Analysis written by R. Tyrrell Rockafellar and published by Springer Science & Business Media. This book was released on 2009-06-26 with total page 747 pages. Available in PDF, EPUB and Kindle. Book excerpt: From its origins in the minimization of integral functionals, the notion of variations has evolved greatly in connection with applications in optimization, equilibrium, and control. This book develops a unified framework and provides a detailed exposition of variational geometry and subdifferential calculus in their current forms beyond classical and convex analysis. Also covered are set-convergence, set-valued mappings, epi-convergence, duality, and normal integrands.
Book Synopsis SIAM Journal on Control and Optimization by : Society for Industrial and Applied Mathematics
Download or read book SIAM Journal on Control and Optimization written by Society for Industrial and Applied Mathematics and published by . This book was released on 2007 with total page 804 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Control of Partial Differential Equations by : Giuseppe Da Prato
Download or read book Control of Partial Differential Equations written by Giuseppe Da Prato and published by CRC Press. This book was released on 1994-08-19 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt: This useful reference provides recent results as well as entirely new material on control problems for partial differential equations.
