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An Error Estimate For The Variational Discretization Of Semilinear Optimal Control Problems In The Presence Of Pointwise Control And State Constraints
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Book Synopsis An Error Estimate for the Variational Discretization of Semilinear Optimal Control Problems in the Presence of Pointwise Control and State Constraints by : Morten Vierling
Download or read book An Error Estimate for the Variational Discretization of Semilinear Optimal Control Problems in the Presence of Pointwise Control and State Constraints written by Morten Vierling and published by . This book was released on 2009 with total page 42 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 Springer Science & Business Media. This book was released on 2012-01-03 with total page 622 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 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 226 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 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.
Book Synopsis Regularization Error Estimates for Semilinear Elliptic Optimal Control Problems with Pointwise State and Control Constraints by : Klaus Krumbiegel
Download or read book Regularization Error Estimates for Semilinear Elliptic Optimal Control Problems with Pointwise State and Control Constraints written by Klaus Krumbiegel and published by . This book was released on 2010 with total page 25 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Journal of Numerical Mathematics by :
Download or read book Journal of Numerical Mathematics written by and published by . This book was released on 2008 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Discretization Error Estimates for State Constrained Optimal Control Problems by : Miloš Tepavčević
Download or read book Discretization Error Estimates for State Constrained Optimal Control Problems written by Miloš Tepavčević and published by . This book was released on 2019 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Numerical Methods for Optimal Control Problems with State Constraints by : Radoslaw Pytlak
Download or read book Numerical Methods for Optimal Control Problems with State Constraints written by Radoslaw Pytlak and published by Springer. This book was released on 2014-03-12 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: While optimality conditions for optimal control problems with state constraints have been extensively investigated in the literature the results pertaining to numerical methods are relatively scarce. This book fills the gap by providing a family of new methods. Among others, a novel convergence analysis of optimal control algorithms is introduced. The analysis refers to the topology of relaxed controls only to a limited degree and makes little use of Lagrange multipliers corresponding to state constraints. This approach enables the author to provide global convergence analysis of first order and superlinearly convergent second order methods. Further, the implementation aspects of the methods developed in the book are presented and discussed. The results concerning ordinary differential equations are then extended to control problems described by differential-algebraic equations in a comprehensive way for the first time in the literature.
Book Synopsis An a Posteriori Error Analysis for Distributed Elliptic Optimal Control Problems with Pointwise State Constraints by :
Download or read book An a Posteriori Error Analysis for Distributed Elliptic Optimal Control Problems with Pointwise State Constraints written by and published by . This book was released on 2007 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis is concerned with the development, analysis, and implementation of an adaptive finite element method for distributed elliptic optimal control problems with pointwise unilateral constraints on the state. In particular, two residual-type a posteriori error estimators will be derived. The first one takes advantage of the modified adjoint state, which is defined as some kind of regularization of the adjoint state. Furthermore, this error estimator will, after minor modification, be transfered to the Lavrentiev regularization of the pure state constrained case. Up to a consistency error and data oscillation, reliability and efficiency results concerning the approximation of the state, the control, and the modified adjoint state can be provided for these error estimators. With two numerical examples, the performance of the adaptive algorithm will be investigated. A benefit compared to an uniform refinement strategy will be noticeable. The second developed a posteriori error estimator results from a measure extension of the discrete measure appearing in the right-hand side of the adjoint state equation to an element in the space of square integrable functions. This error estimator provides, again up to a consistency error and data oscillation, reliability and efficiency for the approximation error in the control, in the state, and in a semi-continuous auxiliary adjoint state. Another numerical example will show that this error estimator might be advantageous.
Book Synopsis Optimal Control of Stochastic Difference Volterra Equations by : Leonid Shaikhet
Download or read book Optimal Control of Stochastic Difference Volterra Equations written by Leonid Shaikhet and published by Springer. This book was released on 2014-11-27 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book showcases a subclass of hereditary systems, that is, systems with behaviour depending not only on their current state but also on their past history; it is an introduction to the mathematical theory of optimal control for stochastic difference Volterra equations of neutral type. As such, it will be of much interest to researchers interested in modelling processes in physics, mechanics, automatic regulation, economics and finance, biology, sociology and medicine for all of which such equations are very popular tools. The text deals with problems of optimal control such as meeting given performance criteria, and stabilization, extending them to neutral stochastic difference Volterra equations. In particular, it contrasts the difference analogues of solutions to optimal control and optimal estimation problems for stochastic integral Volterra equations with optimal solutions for corresponding problems in stochastic difference Volterra equations. Optimal Control of Stochastic Difference Volterra Equations commences with an historical introduction to the emergence of this type of equation with some additional mathematical preliminaries. It then deals with the necessary conditions for optimality in the control of the equations and constructs a feedback control scheme. The approximation of stochastic quasilinear Volterra equations with quadratic performance functionals is then considered. Optimal stabilization is discussed and the filtering problem formulated. Finally, two methods of solving the optimal control problem for partly observable linear stochastic processes, also with quadratic performance functionals, are developed. Integrating the author’s own research within the context of the current state-of-the-art of research in difference equations, hereditary systems theory and optimal control, this book is addressed to specialists in mathematical optimal control theory and to graduate students in pure and applied mathematics and control engineering.
Book Synopsis Estimation and Control Problems for Stochastic Partial Differential Equations by : Pavel S. Knopov
Download or read book Estimation and Control Problems for Stochastic Partial Differential Equations written by Pavel S. Knopov and published by Springer Science & Business Media. This book was released on 2013-09-17 with total page 191 pages. Available in PDF, EPUB and Kindle. Book excerpt: Focusing on research surrounding aspects of insufficiently studied problems of estimation and optimal control of random fields, this book exposes some important aspects of those fields for systems modeled by stochastic partial differential equations. It contains many results of interest to specialists in both the theory of random fields and optimal control theory who use modern mathematical tools for resolving specific applied problems, and presents research that has not previously been covered. More generally, this book is intended for scientists, graduate, and post-graduates specializing in probability theory and mathematical statistics. The models presented describe many processes in turbulence theory, fluid mechanics, hydrology, astronomy, and meteorology, and are widely used in pattern recognition theory and parameter identification of stochastic systems. Therefore, this book may also be useful to applied mathematicians who use probability and statistical methods in the selection of useful signals subject to noise, hypothesis distinguishing, distributed parameter systems optimal control, and more. Material presented in this monograph can be used for education courses on the estimation and control theory of random fields.
Book Synopsis Deterministic and Stochastic Optimal Control and Inverse Problems by : Baasansuren Jadamba
Download or read book Deterministic and Stochastic Optimal Control and Inverse Problems written by Baasansuren Jadamba and published by CRC Press. This book was released on 2021-12-15 with total page 394 pages. Available in PDF, EPUB and Kindle. Book excerpt: Inverse problems of identifying parameters and initial/boundary conditions in deterministic and stochastic partial differential equations constitute a vibrant and emerging research area that has found numerous applications. A related problem of paramount importance is the optimal control problem for stochastic differential equations. This edited volume comprises invited contributions from world-renowned researchers in the subject of control and inverse problems. There are several contributions on optimal control and inverse problems covering different aspects of the theory, numerical methods, and applications. Besides a unified presentation of the most recent and relevant developments, this volume also presents some survey articles to make the material self-contained. To maintain the highest level of scientific quality, all manuscripts have been thoroughly reviewed.
Book Synopsis An a Posteriori Error Analysis for Distributed Elliptic Optimal Control Problems with Pointwise State Constraints by : Michael Kieweg
Download or read book An a Posteriori Error Analysis for Distributed Elliptic Optimal Control Problems with Pointwise State Constraints written by Michael Kieweg and published by . This book was released on 2007 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Error Estimates for Parabolic Optimal Control Problems with Control and State Constraints by :
Download or read book Error Estimates for Parabolic Optimal Control Problems with Control and State Constraints written by and published by . This book was released on 2010 with total page 17 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Sufficient Optimality Conditions for the Moreau-Yosida-type Regularization Concept Applied to Semilinear Elliptic Optimal Control Problems with Pointwise State Constraints by : Klaus Krumbiegel
Download or read book Sufficient Optimality Conditions for the Moreau-Yosida-type Regularization Concept Applied to Semilinear Elliptic Optimal Control Problems with Pointwise State Constraints written by Klaus Krumbiegel and published by . This book was released on 2010 with total page 21 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Mathematical Reviews written by and published by . This book was released on 2005 with total page 1884 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Numerical Analysis of PDE Constrained Optimal Control Problems with Pointwise Inequality Constraints on the State and the Control by :
Download or read book Numerical Analysis of PDE Constrained Optimal Control Problems with Pointwise Inequality Constraints on the State and the Control written by and published by . This book was released on 2011 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt:
