Constrained Optimization and Image Space Analysis (eBook)
XII, 396 Seiten
Springer US (Verlag)
978-0-387-28020-2 (ISBN)
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.
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.
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
| Erscheint lt. Verlag | 27.10.2006 |
|---|---|
| Reihe/Serie | Mathematical Concepts and Methods in Science and Engineering | Mathematical Concepts and Methods in Science and Engineering |
| Zusatzinfo | XII, 396 p. |
| Verlagsort | New York |
| Sprache | englisch |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Angewandte Mathematik |
| Technik ► Bauwesen | |
| Schlagworte | Calculus • combinatorics • Convexity • Design • Mechanics • Optimization • optimization, image space analysis, applications of mathemat • programming |
| ISBN-10 | 0-387-28020-0 / 0387280200 |
| ISBN-13 | 978-0-387-28020-2 / 9780387280202 |
| Haben Sie eine Frage zum Produkt? |
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