Constrained Optimization and Image Space Analysis: Volume 1: Separation of Sets and Optimality Conditions

ISBN-13: 9781441937599 / Angielski / Miękka / 2010 / 396 str.

Franco Giannessi

Opis

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.

Recenzje

From the reviews:

"This is a very substantial and useful monograph ... . it would be an excellent reference in a course at the graduate level in engineering or the advanced undergraduate level in mathematics, as well as for working mathematicians interested in optimization. This book is of unusually fine quality ... it will amply repay the time required. A notable feature of this work is the depth and completeness of coverage of many of the topics. ... Another aspect ... is the extensive use of examples." (Stephen M. Robinson, SIAM Review, Vol. 48 (2), 2006)

Spis treści

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