Author: Christian MeyerPublisher:
ISBN:
Category :
Languages : en
Pages : 25
Book Description
State Constrained Optimal Control of Semilinear Elliptic Equations with Nonlocal Radiation Interface Conditions
Author: Christian MeyerRegularization of State Constrained Elliptic Optimal Control Problems with Nonlocal Radiation Interface Conditions
Author: Christian MeyerTrends in PDE Constrained Optimization
Author: Günter LeugeringPublisher: Springer
ISBN: 3319050834
Category : Mathematics
Languages : en
Pages : 539
Book Description
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.
Variational Analysis and Set Optimization
Author: Akhtar A. KhanPublisher: CRC Press
ISBN: 1351712063
Category : Business & Economics
Languages : en
Pages : 226
Book Description
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.
SIAM Journal on Control and Optimization
Author: Society for Industrial and Applied MathematicsPublisher:
ISBN:
Category : Control theory
Languages : en
Pages : 810
Book Description
Optimal Control of Semilinear Elliptic Equations with Pointwise Constraints on the Gradient of the State
Author: Eduardo CasasAn Extension of Pontryagin's Principle for State-constrained Optimal Control of Semilinear Elliptic Equations and Variational Inequalities
Author: Institut National de Recherche en Informatique et en AutomatiquePublisher:
ISBN:
Category :
Languages : en
Pages : 28
Book Description
Maximum Principle for State-constrained Optimal Control Problems Governed by Quasilinear Elliptic Equations
Author: University of Minnesota. Institute for Mathematics and Its ApplicationsPublisher:
ISBN:
Category :
Languages : en
Pages :
Book Description
Author: Ahmad Ahmad Ali
Author: E. Casas