An Extension of Pontryagin's Principle for State-constrained Optimal Control of Semilinear Elliptic Equations and Variational Inequalities PDF Download

Author: Institut National de Recherche en Informatique et en Automatique
Publisher:
ISBN:
Category :
Languages : en
Pages : 28

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Author: Joseph Frédéric Bonnans
Publisher:
ISBN:
Category : Boundary element methods
Languages : en
Pages : 18

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Abstract: "This paper deals with necessary conditions satisfied by the optimal control of a variational inequality governed by a semilinear operator of elliptic type and a maximal monotone operator in [formula]. A non classical smoothing of allows us to formulate a perturbed problem for which the original control is an [epsilon]-solution. By considering the spike perturbations and applying Ekeland's principle we are able to state approximate optimality conditions in Pontryagin's form. Then passing to the limit we obtain some optimality conditions for the original problem extending those obtained for semilinear elliptic systems and for variational inequalities

Author: K. Malanowski
Publisher: Springer
ISBN: 0387349227
Category : Computers
Languages : en
Pages : 386

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Author: Michael Ruzhansky
Publisher: Birkhäuser
ISBN: 331927466X
Category : Mathematics
Languages : en
Pages : 255

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Book Description
Different facets of interplay between harmonic analysis and approximation theory are covered in this volume. The topics included are Fourier analysis, function spaces, optimization theory, partial differential equations, and their links to modern developments in the approximation theory. The articles of this collection were originated from two events. The first event took place during the 9th ISAAC Congress in Krakow, Poland, 5th-9th August 2013, at the section “Approximation Theory and Fourier Analysis”. The second event was the conference on Fourier Analysis and Approximation Theory in the Centre de Recerca Matemàtica (CRM), Barcelona, during 4th-8th November 2013, organized by the editors of this volume. All articles selected to be part of this collection were carefully reviewed.

Author: Tomáš Roubiček
Publisher: Walter de Gruyter
ISBN: 9783110145427
Category : Mathematics
Languages : en
Pages : 496

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Book Description
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

Author: Society for Industrial and Applied Mathematics
Publisher:
ISBN:
Category : Control theory
Languages : en
Pages : 802

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Author: Tomáš Roubíček
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110590859
Category : Mathematics
Languages : en
Pages : 602

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Book Description
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.

Author: W. Desch
Publisher: Birkhäuser
ISBN: 303488849X
Category : Mathematics
Languages : en
Pages : 308

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Book Description
Consisting of 23 refereed contributions, this volume offers a broad and diverse view of current research in control and estimation of partial differential equations. Topics addressed include, but are not limited to - control and stability of hyperbolic systems related to elasticity, linear and nonlinear; - control and identification of nonlinear parabolic systems; - exact and approximate controllability, and observability; - Pontryagin's maximum principle and dynamic programming in PDE; and - numerics pertinent to optimal and suboptimal control problems. This volume is primarily geared toward control theorists seeking information on the latest developments in their area of expertise. It may also serve as a stimulating reader to any researcher who wants to gain an impression of activities at the forefront of a vigorously expanding area in applied mathematics.

Author: Wolfgang Desch
Publisher: Birkhäuser
ISBN: 303488530X
Category : Mathematics
Languages : en
Pages : 403

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Book Description
22 papers on control of nonlinear partial differential equations highlight the area from a broad variety of viewpoints. They comprise theoretical considerations such as optimality conditions, relaxation, or stabilizability theorems, as well as the development and evaluation of new algorithms. A significant part of the volume is devoted to applications in engineering, continuum mechanics and population biology.

Author: Fredi Tröltzsch
Publisher: American Mathematical Society
ISBN: 1470476444
Category : Mathematics
Languages : en
Pages : 417

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Book Description
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.