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| Author | : Roland Griesse |
| Publisher | : |
| Total Pages | : 194 |
| Release | : 2003 |
| Genre | : |
| ISBN | : |
| Author | : Roland Griesse |
| Publisher | : |
| Total Pages | : 194 |
| Release | : 2003 |
| Genre | : |
| ISBN | : |
| Author | : Roland Griesse |
| Publisher | : |
| Total Pages | : 194 |
| Release | : 2002 |
| Genre | : |
| ISBN | : |
| Author | : John Robert Sesak |
| Publisher | : |
| Total Pages | : 572 |
| Release | : 1974 |
| Genre | : |
| ISBN | : |
| Author | : Lorenz T. Biegler |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 347 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 364255508X |
Optimal design, optimal control, and parameter estimation of systems governed by partial differential equations (PDEs) give rise to a class of problems known as PDE-constrained optimization. The size and complexity of the discretized PDEs often pose significant challenges for contemporary optimization methods. With the maturing of technology for PDE simulation, interest has now increased in PDE-based optimization. The chapters in this volume collectively assess the state of the art in PDE-constrained optimization, identify challenges to optimization presented by modern highly parallel PDE simulation codes, and discuss promising algorithmic and software approaches for addressing them. These contributions represent current research of two strong scientific computing communities, in optimization and PDE simulation. This volume merges perspectives in these two different areas and identifies interesting open questions for further research.
| Author | : Christof Büskens |
| Publisher | : |
| Total Pages | : 24 |
| Release | : 2004 |
| Genre | : |
| ISBN | : |
| Author | : Roland Griesse |
| Publisher | : |
| Total Pages | : 23 |
| Release | : 2018 |
| Genre | : |
| ISBN | : |
This article presents a new area of application for Automatic Differentiation (AD): Computing parametric sensitivities for optimisation problems. For an optimisation problem containing parameters which are not among the optimisation variables, the term parametric sensitivity refers to the derivative of an optimal solution with respect to the parameters. We treat non-linear finite- and infinite-dimensional optimisation problems, in particular optimal control problems involving ordinary differential equations with control and state constraints, and compute their parametric sensitivities using AD. Particular attention is given to the generation of second-order derivatives required in the process.
| Author | : Andrzej Wierzbicki |
| Publisher | : Elsevier Publishing Company |
| Total Pages | : 424 |
| Release | : 1984 |
| Genre | : Technology & Engineering |
| ISBN | : |
Mathematical models. Sensitivity analysis of mathematical models. Optimization and optimal control. Sensitivity analysis of the optimal control systems.
| Author | : Kristian Bredies |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 221 |
| Release | : 2013-06-12 |
| Genre | : Mathematics |
| ISBN | : 3034806310 |
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.
| Author | : Dan Tiba |
| Publisher | : Springer |
| Total Pages | : 166 |
| Release | : 2006-11-14 |
| Genre | : Science |
| ISBN | : 3540467556 |
The book is devoted to the study of distributed control problems governed by various nonsmooth state systems. The main questions investigated include: existence of optimal pairs, first order optimality conditions, state-constrained systems, approximation and discretization, bang-bang and regularity properties for optimal control. In order to give the reader a better overview of the domain, several sections deal with topics that do not enter directly into the announced subject: boundary control, delay differential equations. In a subject still actively developing, the methods can be more important than the results and these include: adapted penalization techniques, the singular control systems approach, the variational inequality method, the Ekeland variational principle. Some prerequisites relating to convex analysis, nonlinear operators and partial differential equations are collected in the first chapter or are supplied appropriately in the text. The monograph is intended for graduate students and for researchers interested in this area of mathematics.
