Skip to main content
SpringerLink
Log in

Principles of Dynamic Optimization

  • Book
  • Jun 2024

Overview

Authors:
  1. Piernicola Bettiol

    1. Department of Mathematics, University of Brest, Brest, France

    View author publications

    You can also search for this author in PubMed   Google Scholar

  2. Richard B. Vinter

    1. Electrical & Electronic Engineering, Imperial College London, London, United Kingdom

    View author publications

    You can also search for this author in PubMed   Google Scholar

  • Discusses numerous recent advances not previously available in book form
  • Includes a comprehensive treatment of dynamic programming based on a study of system invariance
  • Provides a self-contained exposition of non-smooth analysis, emphasizing aspects relevant to optimization

Part of the book series: Springer Monographs in Mathematics (SMM)

Buy print copy

Hardcover Book USD 199.99
Price excludes VAT (USA)
This title has not yet been released. You may pre-order it now and we will ship your order when it is published on 24 Jun 2024.
  • Durable hardcover edition
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Keywords

  • Dynamic Optimization
  • Optimal Control
  • Nonsmooth Analysis
  • Differential Inclusions
  • Hamilton-Jacobi Theory

About this book

This monograph explores key principles in the modern theory of dynamic optimization, incorporating important advances in the field to provide a comprehensive, mathematically rigorous reference. Emphasis is placed on nonsmooth analytic techniques, and an in-depth treatment of necessary conditions, minimizer regularity, and global optimality conditions related to the Hamilton-Jacobi equation is given. New, streamlined proofs of fundamental theorems are incorporated throughout the text that eliminate earlier, cumbersome reductions and constructions. The first chapter offers an extended overview of dynamic optimization and its history that details the shortcomings of the elementary theory and demonstrates how a deeper analysis aims to overcome them. Aspects of dynamic programming well-matched to analytical techniques are considered in the final chapter, including characterization of extended-value functions associated with problems having endpoint and state constraints, inverse verification theorems, sensitivity relationships, and links to the maximum principle.

This text will be a valuable resource for those seeking an understanding of dynamic optimization. The lucid exposition, insights into the field, and comprehensive coverage will benefit postgraduates, researchers, and professionals in system science, control engineering, optimization, and applied mathematics.


Authors and Affiliations

  • Department of Mathematics, University of Brest, Brest, France

    Piernicola Bettiol

  • Electrical & Electronic Engineering, Imperial College London, London, United Kingdom

    Richard B. Vinter

About the authors

Piernicola Bettiol is professor of mathematics at the University of Brest, France. He received a PhD degree in mathematics from the University of Padova and was a Postdoctoral Researcher at Imperial College London. His areas of research are dynamic optimization, control theory, calculus of variations and differential games. 

Richard Vinter is Emeritus Professor of Control Theory at Imperial College, London. He obtained a PhD from Cambridge University and was a Postdoctoral Researcher (Harkness Fellowship) at M.I.T.. His research is in the areas of nonlinear analysis, dynamic optimization, systems theory, differential games, stochastic modelling and estimation.


Bibliographic Information

  • Book Title: Principles of Dynamic Optimization

  • Authors: Piernicola Bettiol, Richard B. Vinter

  • Series Title: Springer Monographs in Mathematics

  • Publisher: Springer Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2024

  • Hardcover ISBN: 978-3-031-50088-6Due: 24 June 2024

  • Softcover ISBN: 978-3-031-50091-6Due: 24 June 2024

  • eBook ISBN: 978-3-031-50089-3Due: 24 June 2024

  • Series ISSN: 1439-7382

  • Series E-ISSN: 2196-9922

  • Edition Number: 1

  • Number of Pages: XVIII, 769

  • Number of Illustrations: 15 b/w illustrations

Publish with us

Policies and ethics

Back to top

Search

Navigation