Principles of Dynamic Optimization / by Piernicola Bettiol, Richard B. Vinter.

Format:

Book

Author/Creator:

Bettiol, Piernicola.

Contributor:

Vinter, R. B. (Richard B.)

Series:

Springer Monographs in Mathematics, 2196-9922

Language:

English

Subjects (All):

Mathematical optimization.

Calculus of variations.

Dynamics.

System theory.

Control theory.

Calculus of Variations and Optimization.

Dynamical Systems.

Systems Theory, Control.

Local Subjects:

Calculus of Variations and Optimization.

Dynamical Systems.

Systems Theory, Control.

Physical Description:

1 online resource (789 pages)

Edition:

1st ed. 2024.

Place of Publication:

Cham : Springer Nature Switzerland : Imprint: Springer, 2024.

Summary:

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.

Contents:

Preface

Overview

Set Convergence, Measurability, and Existence of Minimizers

Variational Principles

Nonsmooth Analysis

Subdifferential Calculus

Differential Inclusions

The Maximum Principle

The Generalized Euler-Lagrange and Hamiltonian Inclusion Conditions

Free End-Time Problems

The Maximum Principle for Problems with Pathwise Constraints

The Euler-Lagrange and Hamiltonian Inclusion Conditions in the Presence of State Constraints

Regularity of Minimizers

Dynamic Programming

Bibliography

Index.

ISBN:

9783031500893

OCLC:

1441720212