Nonconvex optimal control and variational problems Alexander J. Zaslavski

Format:

Book

Author/Creator:

Zaslavski, Alexander J.

Series:

Springer optimization and its applications v. 82

Springer optimization and its applications 1931-6828 v. 82

Language:

English

Subjects (All):

Mathematical optimization.

Variational inequalities (Mathematics).

Mathematics.

mathematics.

applied mathematics.

Medical Subjects:

Mathematics.

Physical Description:

1 online resource

Place of Publication:

New York, NY Springer ©2013

Language Note:

English

System Details:

text file

PDF

Summary:

Nonconvex Optimal Control and Variational Problems is an important contribution to the existing literature in the field and is devoted to the presentation of progress made in the last 15 years of research in the area of optimal control and the calculus of variations. This volume contains a number of results concerning well-posedness of optimal control and variational problems, nonoccurrence of the Lavrentiev phenomenon for optimal control and variational problems, and turnpike properties of approximate solutions of variational problems. Chapter 1 contains an introduction as well as examples of select topics. Chapters 2-5 consider the well-posedness condition using fine tools of general topology and porosity. Chapters 6-8 are devoted to the nonoccurrence of the Lavrentiev phenomenon and contain original results. Chapter 9 focuses on infinite-dimensional linear control problems, and Chapter 10 deals with "good" functions and explores new understandings on the questions of optimality and variational problems. Finally, Chapters 11-12 are centered around the turnpike property, a particular area of expertise for the author. This volume is intended for mathematicians, engineers, and scientists interested in the calculus of variations, optimal control, optimization, and applied functional analysis, as well as both undergraduate and graduate students specializing in those areas. The text devoted to Turnpike properties may be of particular interest to the economics community. Also by Alexander J. Zaslavski: Optimization on Metric and Normed Spaces, © 2010; Structure of Solutions of Variational Problems, © 2013; Turnpike Properties in the Calculus of Variations and Optimal Control, © 2006

Contents:

Introduction Well-posedness of Optimal Control Problems Without Convexity Assumptions Well-posedness and Porosity in Nonconvex Optimal control Well-posedness of Nonconvex Variational Problems Generic Well-posedness Result for a Class of Optimal Control Problems Nonoccurrence of the Lavrentiev Phenomenon for Variational Problems Nonoccurrence of the Lavrentiev Phenomenon in Optimal Control Generic Nonoccurrence of the Lavrentiev Phenomenon Infinite-Dimensional Linear Control Problems Uniform Boundedness of Approximate Solutions of Variational Problems The Turnpike Property for Approximate Solutions of Variational Problems A Turnpike Result for Discrete-Time Optimal Control Systems

Notes:

Includes bibliographical references and index

Print version record

Other Format:

Print version Zaslavski, Alexander J. Nonconvex optimal control and variational problems

ISBN:

9781461473787

1461473780

1461473772

9781461473770

OCLC:

849904649

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