Optimal Control and convex programming
Optimal Control and convex programming

Author: Judah Ben Rosen

Publisher:

Published: 1965

Total Pages: 25

ISBN-13:

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A general type of discrete optimal control problem with both control and state constraints is considered. Necessary conditions for a relative minimum are given (assuming only differentiability) based on the KuhnTucker theory. For a convex function and linear system of differential equations it is shown that these conditions are also sufficient for a global minimum. A computational scheme is described for the state constrained problem where the conditions are sufficient. The scheme is based on a convex programming method and determines first if any admissible control exists, and if so, finds an optimal control. The solution of a four-dimensional system with state constraints is presented in order to illustrate this computational scheme. (Author).

Optimality Conditions in Convex Optimization
Optimality Conditions in Convex Optimization

Author: Anulekha Dhara

Publisher: CRC Press

Published: 2011-10-17

Total Pages: 446

ISBN-13: 1439868220

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Optimality Conditions in Convex Optimization explores an important and central issue in the field of convex optimization: optimality conditions. It brings together the most important and recent results in this area that have been scattered in the literature—notably in the area of convex analysis—essential in developing many of the important results in this book, and not usually found in conventional texts. Unlike other books on convex optimization, which usually discuss algorithms along with some basic theory, the sole focus of this book is on fundamental and advanced convex optimization theory. Although many results presented in the book can also be proved in infinite dimensions, the authors focus on finite dimensions to allow for much deeper results and a better understanding of the structures involved in a convex optimization problem. They address semi-infinite optimization problems; approximate solution concepts of convex optimization problems; and some classes of non-convex problems which can be studied using the tools of convex analysis. They include examples wherever needed, provide details of major results, and discuss proofs of the main results.

State Constrained Optimal Control Problems with States of Low Regularity
State Constrained Optimal Control Problems with States of Low Regularity

Author: Anton Schiela

Publisher:

Published: 2008

Total Pages: 28

ISBN-13:

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Abstract: "We consider first order optimality conditions for state constrained optimal control problems. In particular we study the case where the state equation has not enough regularity to admit existence of a Slater point in function space. We overcome this difficulty by a special transformation. Under a density condition we show existence of Lagrange multipliers, which have a representation via measures and additional regularity properties."

Optimal Control of Nonsmooth Distributed Parameter Systems
Optimal Control of Nonsmooth Distributed Parameter Systems

Author: Dan Tiba

Publisher: Springer

Published: 2006-11-14

Total Pages: 166

ISBN-13: 3540467556

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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.

Regularization Methods for Ill-Posed Optimal Control Problems
Regularization Methods for Ill-Posed Optimal Control Problems

Author: Frank Pörner

Publisher: BoD – Books on Demand

Published: 2018-10-04

Total Pages: 181

ISBN-13: 3958260861

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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.

Convex Optimization
Convex Optimization

Author: Stephen P. Boyd

Publisher: Cambridge University Press

Published: 2004-03-08

Total Pages: 744

ISBN-13: 9780521833783

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Convex optimization problems arise frequently in many different fields. This book provides a comprehensive introduction to the subject, and shows in detail how such problems can be solved numerically with great efficiency. The book begins with the basic elements of convex sets and functions, and then describes various classes of convex optimization problems. Duality and approximation techniques are then covered, as are statistical estimation techniques. Various geometrical problems are then presented, and there is detailed discussion of unconstrained and constrained minimization problems, and interior-point methods. The focus of the book is on recognizing convex optimization problems and then finding the most appropriate technique for solving them. It contains many worked examples and homework exercises and will appeal to students, researchers and practitioners in fields such as engineering, computer science, mathematics, statistics, finance and economics.