Optimization techniques II : discrete and functional optimization / Max Cerf.

Format:

Book

Author/Creator:

Cerf, Max, author.

Series:

Current Natural Sciences Series

Language:

English

Subjects (All):

Applied mathematics.

Physical Description:

1 online resource (478 pages)

Edition:

First edition.

Place of Publication:

Les Ulis, France : EDP Sciences, [2023]

Summary:

This book in two volumes provides an overview of continuous, discrete and functional optimization techniques. This second volume is devoted to discrete optimization (problems with integer variables) and functional optimization (problems where the unknown is a function). The topics covered are: • mixed linear programming: cutting methods and tree methods; • combinatorial optimization based on graphs: path, flow, assignment problems . ; • the computation of variations based on Euler-Lagrange conditions and their extensions; • optimal control based on the Pontryaguin maximum principle and its extensions; • numerical methods: differential equations, direct and indirect methods. The emphasis is on understanding the principles rather than on mathematical rigor. Each concept or algorithm is accompanied by a detailed example to help you grasp the main ideas. This book is the result of 30 years of experience and is intended for students, researchers and engineers wishing to acquire a general knowledge in the field of optimization.

Contents:

Intro

Optimization Techniques II

Preface

Introduction

Table of contents

1. Mixed linear programming

1.1 Formulation

1.2 Cutting methods

1.3 Tree methods

1.4 Applications

1.5 Quadratic problem

1.6 Conclusion

2. Discrete optimization

2.1 Combinatorial problem

2.2 Path problem

2.3 Scheduling problem

2.4 Flow problem

2.5 Assignment problem

2.6 Heuristics

2.7 Conclusion

3. Functional optimization

3.1 Formulation

3.2 Optimality conditions

3.3 Constraints

3.4 Canonical form

3.5 Dynamic system

3.6 Conclusion

4. Optimal control

4.1 Optimality conditions

4.2 Constraints

4.3 Extremals

4.4 Optimality conditions of second order

4.5 Conclusion

5. Numerical methods in optimal control

5.1 Transcription

5.2 Runge-Kutta methods

5.3 Adams methods

5.4 Collocation methods

5.5 Direct methods

5.6 Indirect methods

5.7 Conclusion

Index

Short bibliography.

Notes:

Description based on publisher supplied metadata and other sources.

Description based on print version record.

Includes bibliographical references and index.

ISBN:

9782759831654

2759831655