Nonlinear multiobjective optimization : a generalized homotopy approach /
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boston :
Birkhauser Verlag,
2000
|
| Series: | International series of numerical mathematics
v. 135 International series of numerical mathematics ; v. 135 |
| Subjects: |
Table of Contents:
- 1 Introduction
- 2. Vector Optimization in Industrial Applications
- 2.1. The Design of a Combined-Cycle Power Plant
- 2.2. The Optimal Operating Point of a Recovery-Boiler
- 3. Principles and Methods of Vector Optimization
- 3.1. The Concept of Pareto Optimality
- 3.2. Survey of Methods
- 3.3. A New Stochastic Method for Unconstrained Vector Optimization
- 3.3.1. A Curve of Dominated Points
- 3.3.2. Notions from Probability Theory
- 3.3.3. A Special Stochastic Differential Equation
- 3.3.4. A Stochastic Algorithm for Vector Optimization
- 4. The Connection with Scalar-Valued Optimization
- 4.1. The Karush-Kuhn-Tucker(KKT) Condition for Pareto Optimality
- 4.2. Differential-Topological Notations
- 4.3. The Geometrical Meaning of the Weight Vector
- 4.4. Classification of Efficient Points
- 5. The Manifold of Stationary Points
- 5.1. Karush-Kuhn-Tucker Points as a Differentiable Manifold M
- 5.2. Criteria for the Rank Condition
- 5.2.1. A Necessary and Sufficient Criterion
- 5.2.2. Interpretation in View of Optimization
- 5.2.3. Variability of the Weight Vector
- 5.3. A Special Class of Local Charts
- 6. Homotype Strategies
- 6.1. Method I: Local Exploration of M
- 6.1.1. Method Principle
- 6.1.2. Comparison with Classical Homotopy Method
- 6.1.3. Homogeneous Discretization of the Efficient Set
- 6.1.4. Numerical Algorithm
- 6.2. Method II: Purposeful Change of the Weights
- 6.2.1. Significance of the Weight Vector for the User
- 6.2.2. Principle of the Procedure
- 6.2.3. Numerical Algorithm
- 7. Numerical Results
- 7.1. Example 1 (academic)
- 7.2. Example 2: Design of a Combined-Cycle Power Plant
- 7.3. Example 3: The Optimal Operating Point of a Recovery-Boiler.