Giannessi Constrained Optimization and Image Space Analysis

Volume 1: Separation of Sets and Optimality Conditions
2005
ISBN: 978-0-387-28020-2
Verlag: Springer US
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 49, 396 Seiten, eBook

Reihe: Mathematical Concepts and Methods in Science and Engineering

Over the last twenty years, Professor Franco Giannessi, a highly respected researcher, has been working on an approach to optimization theory based on image space analysis. His theory has been elaborated by many other researchers in a wealth of papers. Constrained Optimization and Image Space Analysis unites his results and presents optimization theory and variational inequalities in their light.

It presents a new approach to the theory of constrained extremum problems, including Mathematical Programming, Calculus of Variations and Optimal Control Problems. Such an approach unifies the several branches: Optimality Conditions, Duality, Penalizations, Vector Problems, Variational Inequalities and Complementarity Problems. The applications benefit from a unified theory.

Zielgruppe

Research

Autoren/Hrsg.

Giannessi, Franco

Inhaltsverzeichnis

Chapter 1. Introduction

1.1. Constrained Extremum Problems

1.2. Special Extremum Problems

1.3. Variational Inequalities, Complernentarity Problems and Generalized Systems

1.4. Optimal Design of an Underwater Pipeline

1.5. Further Problems in Applied Mechanics

1.6. Equilibrium Flows in a Network

1.7. Testing Statistical Hypotheses

1.8. Vector Problems from Industry

1.9. Comments

References

Chapter 2. Elements of Convex Analysis and Separation

2.1. Convex Sets and Cones

2.2. Linear Support and Separation

2.3. Convex Functions

2.4. Some Extensions of Convexity

2.5. Comments

References

Chapter 3. Introduction to Image Space Analysis

3.1. Semidifferentiability

3.2. Image Problem

3.3. Stationarity

3.4. Sonic Examples

3.5. Comments

References

Chapter 4. Alternative and Separation

4.1. Introduction

4.2. Separation Functions

4.3. Special Separation Functions

4.4. A General Setting for a Theorem of the Alternative

4.5. Special Theorems of the Alternative

4.6. A Special Separation Theorem

4.7. Theorems of the Alternative for Multifunctions

4.8. Cone Multifunctions

4.9. Systems of Intersection Type

4.10. Comments

References

Chapter 5. Optimality Conditions. Preliminary Results

5.1. Introduction

5.2. Weak Separation and Sufficient Conditions

5.3. Weak Separation and Necessary Conditioim

5.4. Sonic Applications

5.5. Reciprocal Problems

5.6. Connections between Discrete and Continuous Problems

5.7 Comments

References

Glossary of Notation

Subject Index